EQUATION 1

Regression

Notes
Output Created 19-OCT-2004 09:31:30
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D Dl Dsq TO Dl2/ STATISTICS = all/
DEPENDENT = fH/ METHOD = STEPWISE.
Resources Memory Required 3684 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,05

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 DL2 , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
2 D2R , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
3 DL , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
a Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,955(a) ,913 ,912 ,378211 ,913 3636,365 1 348 ,000 -678,617 ,088 30,184 -670,902(b)
2 ,956(c) ,915 ,914 ,374301 ,002 8,309 1 347 ,004 -684,900 ,087 23,386 -673,326(b)
3 ,959(d) ,919 ,918 ,364963 ,004 18,984 1 346 ,000 -701,594 ,083 6,278 -686,163(b)
a Predictors: (Constant), DL2
b Multicollinearity is present. The following variables were not included in the full model used for calculation of the Mallows' Prediction Criterion: D, DL, DR
c Predictors: (Constant), DL2, D2R
d Predictors: (Constant), DL2, D2R, DL

ANOVA(d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 520,159 1 520,159 3636,365 ,000(a)
Residual 49,779 348 ,143

Total 569,938 349


2 Regression 521,323 2 260,662 1860,525 ,000(b)
Residual 48,615 347 ,140

Total 569,938 349


3 Regression 523,852 3 174,617 1310,960 ,000(c)
Residual 46,087 346 ,133

Total 569,938 349


a Predictors: (Constant), DL2
b Predictors: (Constant), DL2, D2R
c Predictors: (Constant), DL2, D2R, DL
d Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) 13,076 ,121

107,861 ,000 12,837 13,314




DL2 -1,329 ,022 -,955 ,016 -60,302 ,000 -1,372 -1,286 -,955 -,955 -,955 1,000 1,000
2 (Constant) 13,939 ,323

43,202 ,000 13,304 14,574




DL2 -1,615 ,101 -1,161 ,073 -15,911 ,000 -1,814 -1,415 -,955 -,649 -,249 ,046 21,647
D2R 6,132E-03 ,002 ,210 ,073 2,883 ,004 ,002 ,010 -,923 ,153 ,045 ,046 21,647
3 (Constant) -5,372 4,443

-1,209 ,228 -14,111 3,368




DL2 -7,525 1,360 -5,410 ,978 -5,532 ,000 -10,201 -4,850 -,955 -,285 -,085 ,000 4091,549
D2R 3,608E-02 ,007 1,237 ,246 5,025 ,000 ,022 ,050 -,923 ,261 ,077 ,004 259,308
DL -20,696 4,750 -3,255 ,747 -4,357 ,000 -30,038 -11,353 ,955 -,228 -,067 ,000 2387,548
a Dependent Variable: FH





Excluded Variables(d)

Beta In t Sig. Partial Correlation Collinearity Statistics
Model Tolerance VIF Minimum Tolerance
1 D ,075(a) 1,131 ,259 ,061 5,749E-02 17,394 5,749E-02
DL ,339(a) 1,519 ,130 ,081 5,017E-03 199,314 5,017E-03
DSQ ,024(a) ,635 ,526 ,034 ,172 5,810 ,172
DCU ,005(a) ,196 ,844 ,011 ,333 3,001 ,333
DR ,483(a) 2,517 ,012 ,134 6,699E-03 149,284 6,699E-03
D2R ,210(a) 2,883 ,004 ,153 4,620E-02 21,647 4,620E-02
2 D -,742(b) -4,279 ,000 -,224 7,791E-03 128,351 1,898E-03
DL -3,255(b) -4,357 ,000 -,228 4,188E-04 2387,548 2,444E-04
DSQ -,323(b) -4,120 ,000 -,216 3,827E-02 26,127 5,141E-03
DCU -,183(b) -3,906 ,000 -,205 ,107 9,305 9,612E-03
DR -10,271(b) -4,445 ,000 -,232 4,367E-05 22897,846 4,367E-05
3 D 3,934(c) 1,237 ,217 ,066 2,307E-05 43340,392 1,240E-06
DSQ ,813(c) 1,395 ,164 ,075 6,865E-04 1456,679 6,950E-06
DCU ,329(c) 1,526 ,128 ,082 5,004E-03 199,856 1,540E-05
DR -9,826(c) -,854 ,394 -,046 1,768E-06 565614,844 1,627E-06
a Predictors in the Model: (Constant), DL2
b Predictors in the Model: (Constant), DL2, D2R
c Predictors in the Model: (Constant), DL2, D2R, DL
d Dependent Variable: FH

Coefficient Correlations(a)
Model DL2 D2R DL
1 Correlations DL2 1,000

Covariances DL2 4,856E-04

2 Correlations DL2 1,000 -,977
D2R -,977 1,000
Covariances DL2 1,030E-02 -2,108E-04
D2R -2,108E-04 4,525E-06
3 Correlations DL2 1,000 -,975 ,997
D2R -,975 1,000 -,957
DL ,997 -,957 1,000
Covariances DL2 1,850 -9,524E-03 6,444
D2R -9,524E-03 5,153E-05 -3,264E-02
DL 6,444 -3,264E-02 22,563
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows DL2 FH D DL DSQ DCU DR D2R
1 DL2 1,000(xx) ,955(xy) ,971(x~) ,997(x~) ,910(x~) ,817(x~) -,997(x~) -,977(x~)
FH -,955(yx) ,087(yy) ,004(y~) ,002(y~) ,004(y~) ,002(y~) ,003(y~) ,010(y~)
D -,971(~x) ,004(~y) ,057(~~) ,017 ,099 ,134 ,019 ,048
DL -,997(~x) ,002(~y) ,017 ,005(~~) ,029 ,039 ,006 ,015
DSQ -,910(~x) ,004(~y) ,099 ,029 ,172(~~) ,238 ,031 ,079
DCU -,817(~x) ,002(~y) ,134 ,039 ,238 ,333(~~) ,041 ,102
DR ,997(~x) ,003(~y) ,019 ,006 ,031 ,041 ,007(~~) ,018
D2R ,977(~x) ,010(~y) ,048 ,015 ,079 ,102 ,018 ,046(~~)
2 DL2 21,647(xx) 1,161(xy) 1,984(x~) 1,306(x~) 2,572(x~) 2,976(x~) -,626(x~) -21,141
FH -1,161(yx) ,085(yy) -,006(y~) -,001(y~) -,012(y~) -,020(y~) ,000(y~) ,210(yx)
D -1,984(~x) -,006(~y) ,008(~~) ,002 ,017 ,029 ,001 1,037(~x)
DL -1,306(~x) -,001(~y) ,002 ,000(~~) ,004 ,007 ,000 ,316(~x)
DSQ -2,572(~x) -,012(~y) ,017 ,004 ,038(~~) ,064 ,001 1,702(~x)
DCU -2,976(~x) -,020(~y) ,029 ,007 ,064 ,107(~~) ,002 2,211(~x)
DR ,626(~x) ,000(~y) ,001 ,000 ,001 ,002 ,000(~~) ,380(~x)
D2R -21,141 -,210(xy) -1,037(x~) -,316(x~) -1,702(x~) -2,211(x~) -,380(x~) 21,647(xx)
3 DL2 4091,549(xx) 5,410(xy) -3,639(x~) 3117,224 -9,796(x~) -17,446(x~) -1,039(x~) -1004,634
FH -5,410(yx) ,081(yy) ,000(y~) -3,255(yx) ,001(y~) ,002(y~) ,000(y~) 1,237(yx)
D 3,639(~x) ,000(~y) ,000(~~) 4,307(~x) ,000 ,000 ,000 -,321(~x)
DL 3117,224 3,255(xy) -4,307(x~) 2387,548(xx) -9,473(x~) -15,641(x~) -,316(x~) -753,278
DSQ 9,796(~x) ,001(~y) ,000 9,473(~x) ,001(~~) ,002 ,000 -1,287(~x)
DCU 17,446(~x) ,002(~y) ,000 15,641(~x) ,002 ,005(~~) ,000 -2,724(~x)
DR 1,039(~x) ,000(~y) ,000 ,316(~x) ,000 ,000 ,000(~~) ,280(~x)
D2R -1004,634 -1,237(xy) ,321(x~) -753,278 1,287(x~) 2,724(x~) -,280(x~) 259,308(xx)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
x~ Row variable is an independent variable, column variable is an excluded independent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
y~ Row variable is the dependent variable, column variable is an excluded independent variable.
~x Row variable is an excluded independent variable, column variable is an independent variable.
~y Row variable is an excluded independent variable, column variable is the dependent variable.
~~ This variable is an excluded predictor.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) DL2 D2R DL
1 1 1,986 1,000 ,01 ,01

2 1,400E-02 11,909 ,99 ,99

2 1 2,930 1,000 ,00 ,00 ,00
2 6,904E-02 6,515 ,03 ,00 ,05
3 8,426E-04 58,970 ,97 1,00 ,95
3 1 3,923 1,000 ,00 ,00 ,00 ,00
2 7,583E-02 7,193 ,00 ,00 ,00 ,00
3 9,290E-04 64,984 ,01 ,00 ,07 ,00
4 1,918E-06 1430,288 ,99 1,00 ,92 1,00
a Dependent Variable: FH

EQUATION 2

Regression

Notes
Output Created 19-OCT-2004 09:31:30
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D Dl D2H TO D2l/ STATISTICS = all/
DEPENDENT = fH/ METHOD = STEPWISE.
Resources Memory Required 12980 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,06

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 HL2 , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
2 DH , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
3 D2H2 , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
a Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,971(a) ,943 ,943 ,305705 ,943 5750,504 1 348 ,000 -827,600 ,058 76,841 -819,885(b)
2 ,975(c) ,950 ,950 ,286445 ,007 49,370 1 347 ,000 -872,158 ,051 26,174 -860,585(b)
3 ,975(d) ,951 ,951 ,283553 ,001 8,115 1 346 ,005 -878,273 ,050 19,691 -862,841(b)
a Predictors: (Constant), HL2
b Multicollinearity is present. The following variables were not included in the full model used for calculation of the Mallows' Prediction Criterion: D, DL, D2H, D2HL, DSQ, DR, D2R, DL2, DH, DH2, HR, DHR, HL, HL2
c Predictors: (Constant), HL2, DH
d Predictors: (Constant), HL2, DH, D2H2

ANOVA(d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 537,416 1 537,416 5750,504 ,000(a)
Residual 32,522 348 9,346E-02

Total 569,938 349


2 Regression 541,467 2 270,733 3299,579 ,000(b)
Residual 28,472 347 8,205E-02

Total 569,938 349


3 Regression 542,119 3 180,706 2247,529 ,000(c)
Residual 27,819 346 8,040E-02

Total 569,938 349


a Predictors: (Constant), HL2
b Predictors: (Constant), HL2, DH
c Predictors: (Constant), HL2, DH, D2H2
d Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) -1,512 ,099

-15,319 ,000 -1,706 -1,318




HL2 1,111 ,015 ,971 ,013 75,832 ,000 1,082 1,139 ,971 ,971 ,971 1,000 1,000
2 (Constant) -,488 ,172

-2,831 ,005 -,828 -,149




HL2 ,850 ,040 ,743 ,035 21,451 ,000 ,772 ,928 ,971 ,755 ,257 ,120 8,329
DH ,509 ,072 ,243 ,035 7,026 ,000 ,367 ,652 ,940 ,353 ,084 ,120 8,329
3 (Constant) ,114 ,272

,421 ,674 -,420 ,649




HL2 ,615 ,091 ,538 ,080 6,752 ,000 ,436 ,795 ,971 ,341 ,080 ,022 44,996
DH 1,421 ,328 ,679 ,157 4,331 ,000 ,776 2,067 ,940 ,227 ,051 ,006 174,433
D2H2 -,138 ,048 -,256 ,090 -2,849 ,005 -,233 -,043 ,819 -,151 -,034 ,017 57,356
a Dependent Variable: FH





Excluded Variables(d)

Beta In t Sig. Partial Correlation Collinearity Statistics
Model Tolerance VIF Minimum Tolerance
1 D ,223(a) 6,956 ,000 ,350 ,140 7,140 ,140
DL ,259(a) 5,575 ,000 ,287 6,982E-02 14,323 6,982E-02
D2H ,148(a) 6,648 ,000 ,336 ,295 3,391 ,295
D2HL ,360(a) 4,912 ,000 ,255 2,861E-02 34,954 2,861E-02
DSQ ,161(a) 6,949 ,000 ,350 ,269 3,714 ,269
DCU ,121(a) 6,581 ,000 ,333 ,436 2,294 ,436
DR -,094(a) -1,734 ,084 -,093 5,560E-02 17,985 5,560E-02
D2R ,079(a) 1,776 ,077 ,095 8,310E-02 12,034 8,310E-02
DL2 -,216(a) -4,111 ,000 -,216 5,682E-02 17,601 5,682E-02
H2 ,292(a) 5,307 ,000 ,274 5,031E-02 19,876 5,031E-02
DH ,243(a) 7,026 ,000 ,353 ,120 8,329 ,120
DH2 ,180(a) 6,333 ,000 ,322 ,182 5,507 ,182
D2H2 ,124(a) 6,149 ,000 ,313 ,365 2,739 ,365
HR ,367(a) 6,126 ,000 ,312 4,134E-02 24,190 4,134E-02
DHR ,198(a) 4,641 ,000 ,242 8,483E-02 11,789 8,483E-02
D2HR ,157(a) 4,919 ,000 ,255 ,151 6,633 ,151
HDD -,085(a) -6,365 ,000 -,323 ,818 1,222 ,818
HDD2 -,119(a) -4,610 ,000 -,240 ,234 4,275 ,234
HL -1,275(a) -6,017 ,000 -,307 3,313E-03 301,797 3,313E-03
D2L ,259(a) 5,575 ,000 ,287 6,982E-02 14,323 6,982E-02
2 D ,104(b) 1,246 ,214 ,067 2,074E-02 48,223 1,778E-02
DL ,066(b) 1,029 ,304 ,055 3,471E-02 28,811 3,471E-02
D2H -,221(b) -1,574 ,116 -,084 7,298E-03 137,028 2,971E-03
D2HL ,075(b) ,825 ,410 ,044 1,720E-02 58,126 1,720E-02
DSQ ,058(b) ,632 ,528 ,034 1,715E-02 58,310 7,647E-03
DCU -,021(b) -,334 ,738 -,018 3,618E-02 27,640 9,965E-03
DR -,025(b) -,489 ,625 -,026 5,350E-02 18,690 4,595E-02
D2R ,006(b) ,145 ,885 ,008 7,795E-02 12,829 3,945E-02
DL2 -,050(b) -,857 ,392 -,046 4,230E-02 23,639 4,230E-02
H2 -,045(b) -,482 ,630 -,026 1,681E-02 59,475 1,681E-02
DH2 -,295(b) -2,211 ,028 -,118 8,011E-03 124,823 5,296E-03
D2H2 -,256(b) -2,849 ,005 -,151 1,743E-02 57,356 5,733E-03
HR ,139(b) 1,616 ,107 ,087 1,943E-02 51,454 9,408E-03
DHR ,055(b) 1,112 ,267 ,060 5,887E-02 16,985 2,423E-02
D2HR ,051(b) 1,361 ,174 ,073 ,103 9,723 3,266E-02
HDD -,029(b) -1,279 ,202 -,069 ,282 3,544 3,462E-02
HDD2 -,032(b) -1,080 ,281 -,058 ,162 6,154 8,340E-02
HL -,396(b) -1,248 ,213 -,067 1,428E-03 700,245 1,136E-03
D2L ,066(b) 1,029 ,304 ,055 3,471E-02 28,811 3,471E-02
3 D -,014(c) -,153 ,878 -,008 1,579E-02 63,326 2,476E-03
DL -,055(c) -,707 ,480 -,038 2,348E-02 42,597 3,037E-03
D2H ,266(c) 1,151 ,251 ,062 2,633E-03 379,769 2,633E-03
D2HL -,078(c) -,738 ,461 -,040 1,264E-02 79,093 3,517E-03
DSQ ,056(c) ,619 ,536 ,033 1,715E-02 58,313 3,346E-03
DCU ,090(c) 1,245 ,214 ,067 2,722E-02 36,734 5,323E-03
DR ,059(c) ,999 ,318 ,054 4,112E-02 24,321 4,271E-03
D2R ,054(c) 1,185 ,237 ,064 6,895E-02 14,503 5,280E-03
DL2 ,060(c) ,860 ,391 ,046 2,927E-02 34,162 3,479E-03
H2 -,013(c) -,145 ,885 -,008 1,657E-02 60,349 5,528E-03
DH2 -,116(c) -,716 ,474 -,039 5,377E-03 185,992 4,370E-03
HR ,100(c) 1,159 ,247 ,062 1,887E-02 53,003 4,926E-03
DHR ,063(c) 1,288 ,199 ,069 5,869E-02 17,040 5,687E-03
D2HR ,053(c) 1,429 ,154 ,077 ,103 9,726 5,636E-03
HDD ,030(c) ,970 ,333 ,052 ,145 6,895 1,995E-03
HDD2 ,043(c) 1,081 ,280 ,058 9,040E-02 11,063 2,684E-03
HL -,292(c) -,921 ,358 -,050 1,407E-03 710,716 1,026E-03
D2L -,055(c) -,707 ,480 -,038 2,348E-02 42,597 3,037E-03
a Predictors in the Model: (Constant), HL2
b Predictors in the Model: (Constant), HL2, DH
c Predictors in the Model: (Constant), HL2, DH, D2H2
d Dependent Variable: FH

Coefficient Correlations(a)
Model HL2 DH D2H2
1 Correlations HL2 1,000

Covariances HL2 2,145E-04

2 Correlations HL2 1,000 -,938
DH -,938 1,000
Covariances HL2 1,569E-03 -2,692E-03
DH -2,692E-03 5,249E-03
3 Correlations HL2 1,000 -,969 ,903
DH -,969 1,000 -,976
D2H2 ,903 -,976 1,000
Covariances HL2 8,304E-03 -2,898E-02 3,983E-03
DH -2,898E-02 ,108 -1,551E-02
D2H2 3,983E-03 -1,551E-02 2,344E-03
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows HL2 FH D DL D2H D2HL DSQ DCU DR D2R DL2 H2 DH DH2 D2H2 HR DHR D2HR HDD HDD2 HL D2L
1 HL2 1,000(xx) -,971(xy) -,927(x~) -,964(x~) -,840(x~) -,986(x~) -,855(x~) -,751(x~) ,972(x~) ,958(x~) ,971(x~) -,975(x~) -,938(x~) -,905(x~) -,797(x~) ,979(x~) ,957(x~) ,922(x~) -,427(x~) ,875(x~) -,998(x~) -,964(x~)
FH ,971(yx) ,057(yy) ,031(y~) ,018(y~) ,044(y~) ,010(y~) ,043(y~) ,053(y~) -,005(y~) ,007(y~) -,012(y~) ,015(y~) ,029(y~) ,033(y~) ,045(y~) ,015(y~) ,017(y~) ,024(y~) -,070(y~) -,028(y~) -,004(y~) ,018(y~)
D ,927(~x) ,031(~y) ,140(~~) ,091 ,186 ,055 ,189 ,231 -,048 -,012 -,070 ,046 ,120 ,131 ,194 ,037 ,026 ,038 -,324 -,144 -,011 ,091
DL ,964(~x) ,018(~y) ,091 ,070(~~) ,099 ,044 ,112 ,129 -,051 -,036 -,061 ,015 ,065 ,063 ,096 ,011 -,007 -,006 -,234 -,122 -,003 ,070
D2H ,840(~x) ,044(~y) ,186 ,099 ,295(~~) ,057 ,276 ,354 -,024 ,036 -,063 ,093 ,186 ,223 ,325 ,072 ,078 ,106 -,381 -,134 -,021 ,099
D2HL ,986(~x) ,010(~y) ,055 ,044 ,057 ,029(~~) ,067 ,076 -,035 -,028 -,040 ,005 ,037 ,034 ,054 ,003 -,010 -,012 -,145 -,078 -,001 ,044
DSQ ,855(~x) ,043(~y) ,189 ,112 ,276 ,067 ,269(~~) ,339 -,045 ,009 -,080 ,075 ,174 ,200 ,296 ,058 ,054 ,076 -,409 -,162 -,017 ,112
DCU ,751(~x) ,053(~y) ,231 ,129 ,354 ,076 ,339 ,436(~~) -,043 ,024 -,087 ,097 ,219 ,256 ,385 ,073 ,073 ,101 -,474 -,174 -,022 ,129
DR -,972(~x) -,005(~y) -,048 -,051 -,024 -,035 -,045 -,043 ,056(~~) ,060 ,053 ,015 -,016 -,001 -,012 ,015 ,041 ,053 ,151 ,101 -,004 -,051
D2R -,958(~x) ,007(~y) -,012 -,036 ,036 -,028 ,009 ,024 ,060 ,083(~~) ,047 ,042 ,025 ,050 ,055 ,040 ,074 ,098 ,081 ,083 -,011 -,036
DL2 -,971(~x) -,012(~y) -,070 -,061 -,063 -,040 -,080 -,087 ,053 ,047 ,057(~~) -,001 -,042 -,034 -,056 ,000 ,022 ,027 ,195 ,112 ,000 -,061
H2 ,975(~x) ,015(~y) ,046 ,015 ,093 ,005 ,075 ,097 ,015 ,042 -,001 ,050(~~) ,063 ,086 ,110 ,043 ,057 ,075 -,087 -,017 -,012 ,015
DH ,938(~x) ,029(~y) ,120 ,065 ,186 ,037 ,174 ,219 -,016 ,025 -,042 ,063 ,120(~~) ,144 ,204 ,051 ,056 ,076 -,254 -,093 -,015 ,065
DH2 ,905(~x) ,033(~y) ,131 ,063 ,223 ,034 ,200 ,256 -,001 ,050 -,034 ,086 ,144 ,182(~~) ,252 ,069 ,083 ,110 -,263 -,082 -,020 ,063
D2H2 ,797(~x) ,045(~y) ,194 ,096 ,325 ,054 ,296 ,385 -,012 ,055 -,056 ,110 ,204 ,252 ,365(~~) ,084 ,097 ,130 -,383 -,122 -,025 ,096
HR -,979(~x) ,015(~y) ,037 ,011 ,072 ,003 ,058 ,073 ,015 ,040 ,000 ,043 ,051 ,069 ,084 ,041(~~) ,056 ,074 -,072 -,015 -,012 ,011
DHR -,957(~x) ,017(~y) ,026 -,007 ,078 -,010 ,054 ,073 ,041 ,074 ,022 ,057 ,056 ,083 ,097 ,056 ,085(~~) ,113 -,026 ,025 -,016 -,007
D2HR -,922(~x) ,024(~y) ,038 -,006 ,106 -,012 ,076 ,101 ,053 ,098 ,027 ,075 ,076 ,110 ,130 ,074 ,113 ,151(~~) -,044 ,029 -,021 -,006
HDD ,427(~x) -,070(~y) -,324 -,234 -,381 -,145 -,409 -,474 ,151 ,081 ,195 -,087 -,254 -,263 -,383 -,072 -,026 -,044 ,818(~~) ,407 ,021 -,234
HDD2 -,875(~x) -,028(~y) -,144 -,122 -,134 -,078 -,162 -,174 ,101 ,083 ,112 -,017 -,093 -,082 -,122 -,015 ,025 ,029 ,407 ,234(~~) ,004 -,122
HL ,998(~x) -,004(~y) -,011 -,003 -,021 -,001 -,017 -,022 -,004 -,011 ,000 -,012 -,015 -,020 -,025 -,012 -,016 -,021 ,021 ,004 ,003(~~) -,003
D2L ,964(~x) ,018(~y) ,091 ,070 ,099 ,044 ,112 ,129 -,051 -,036 -,061 ,015 ,065 ,063 ,096 ,011 -,007 -,006 -,234 -,122 -,003 ,070(~~)
2 HL2 8,329(xx) -,743(xy) ,008(x~) -,457(x~) ,612(x~) -,696(x~) ,504(x~) ,961(x~) ,848(x~) 1,152(x~) ,645(x~) -,479(x~) -7,813 ,223(x~) ,800(x~) 1,380(x~) 1,393(x~) 1,514(x~) -2,408(x~) ,152(x~) -1,116(x~) -,457(x~)
FH ,743(yx) ,050(yy) ,002(y~) ,002(y~) -,002(y~) ,001(y~) ,001(y~) -,001(y~) -,001(y~) ,000(y~) -,002(y~) -,001(y~) ,243(yx) -,002(y~) -,004(y~) ,003(y~) ,003(y~) ,005(y~) -,008(y~) -,005(y~) -,001(y~) ,002(y~)
D -,008(~x) ,002(~y) ,021(~~) ,026 ,001 ,019 ,016 ,012 -,032 -,037 -,029 -,017 ,997(~x) -,012 -,009 -,014 -,030 -,037 -,071 -,051 ,004 ,026
DL ,457(~x) ,002(~y) ,026 ,035(~~) -,001 ,024 ,018 ,010 -,043 -,050 -,038 -,019 ,541(~x) -,015 -,014 -,017 -,037 -,047 -,097 -,072 ,005 ,035
D2H -,612(~x) -,002(~y) ,001 -,001 ,007(~~) ,000 ,007 ,015 ,000 -,003 ,001 -,005 1,548(~x) ,000 ,009 -,007 -,008 -,011 ,012 ,010 ,002 -,001
D2HL ,696(~x) ,001(~y) ,019 ,024 ,000 ,017(~~) ,013 ,009 -,030 -,035 -,027 -,014 ,308(~x) -,011 -,009 -,013 -,027 -,035 -,067 -,050 ,004 ,024
DSQ -,504(~x) ,001(~y) ,016 ,018 ,007 ,013 ,017(~~) ,021 -,022 -,027 -,019 -,017 1,449(~x) -,010 ,000 -,016 -,027 -,034 -,041 -,028 ,005 ,018
DCU -,961(~x) -,001(~y) ,012 ,010 ,015 ,009 ,021 ,036(~~) -,014 -,022 -,011 -,019 1,825(~x) -,007 ,012 -,021 -,029 -,037 -,011 -,005 ,006 ,010
DR -,848(~x) -,001(~y) -,032 -,043 ,000 -,030 -,022 -,014 ,054(~~) ,064 ,047 ,024 -,132(~x) ,018 ,015 ,022 ,049 ,063 ,118 ,089 -,006 -,043
D2R -1,152(~x) ,000(~y) -,037 -,050 -,003 -,035 -,027 -,022 ,064 ,078(~~) ,055 ,029 ,207(~x) ,020 ,013 ,030 ,063 ,082 ,134 ,102 -,008 -,050
DL2 -,645(~x) -,002(~y) -,029 -,038 ,001 -,027 -,019 -,011 ,047 ,055 ,042(~~) ,021 -,348(~x) ,016 ,015 ,018 ,041 ,053 ,107 ,080 -,005 -,038
H2 ,479(~x) -,001(~y) -,017 -,019 -,005 -,014 -,017 -,019 ,024 ,029 ,021 ,017(~~) ,528(~x) ,010 ,002 ,016 ,028 ,035 ,047 ,032 -,005 -,019
DH -7,813 -,243(xy) -,997(x~) -,541(x~) -1,548(x~) -,308(x~) -1,449(x~) -1,825(x~) ,132(x~) -,207(x~) ,348(x~) -,528(x~) 8,329(xx) -1,202(x~) -1,702(x~) -,427(x~) -,465(x~) -,632(x~) 2,113(x~) ,771(x~) ,125(x~) -,541(x~)
DH2 -,223(~x) -,002(~y) -,012 -,015 ,000 -,011 -,010 -,007 ,018 ,020 ,016 ,010 1,202(~x) ,008(~~) ,007 ,007 ,015 ,019 ,042 ,029 -,002 -,015
D2H2 -,800(~x) -,004(~y) -,009 -,014 ,009 -,009 ,000 ,012 ,015 ,013 ,015 ,002 1,702(~x) ,007 ,017(~~) -,003 ,002 ,001 ,049 ,035 ,001 -,014
HR -1,380(~x) ,003(~y) -,014 -,017 -,007 -,013 -,016 -,021 ,022 ,030 ,018 ,016 ,427(~x) ,007 -,003 ,019(~~) ,032 ,042 ,036 ,025 -,005 -,017
DHR -1,393(~x) ,003(~y) -,030 -,037 -,008 -,027 -,027 -,029 ,049 ,063 ,041 ,028 ,465(~x) ,015 ,002 ,032 ,059(~~) ,077 ,092 ,068 -,009 -,037
D2HR -1,514(~x) ,005(~y) -,037 -,047 -,011 -,035 -,034 -,037 ,063 ,082 ,053 ,035 ,632(~x) ,019 ,001 ,042 ,077 ,103(~~) ,116 ,087 -,011 -,047
HDD 2,408(~x) -,008(~y) -,071 -,097 ,012 -,067 -,041 -,011 ,118 ,134 ,107 ,047 -2,113(~x) ,042 ,049 ,036 ,092 ,116 ,282(~~) ,211 -,011 -,097
HDD2 -,152(~x) -,005(~y) -,051 -,072 ,010 -,050 -,028 -,005 ,089 ,102 ,080 ,032 -,771(~x) ,029 ,035 ,025 ,068 ,087 ,211 ,162(~~) -,007 -,072
HL 1,116(~x) -,001(~y) ,004 ,005 ,002 ,004 ,005 ,006 -,006 -,008 -,005 -,005 -,125(~x) -,002 ,001 -,005 -,009 -,011 -,011 -,007 ,001(~~) ,005
D2L ,457(~x) ,002(~y) ,026 ,035 -,001 ,024 ,018 ,010 -,043 -,050 -,038 -,019 ,541(~x) -,015 -,014 -,017 -,037 -,047 -,097 -,072 ,005 ,035(~~)
3 HL2 44,996(xx) -,538(xy) ,434(x~) ,185(x~) ,199(x~) -,288(x~) ,510(x~) ,387(x~) ,174(x~) ,577(x~) -,046(x~) -,573(x~) -85,855 -,087(x~) 45,859 1,524(x~) 1,310(x~) 1,478(x~) -4,651(x~) -1,474(x~) -1,144(x~) ,185(x~)
FH ,538(yx) ,049(yy) ,000(y~) -,001(y~) ,001(y~) -,001(y~) ,001(y~) ,002(y~) ,002(y~) ,004(y~) ,002(y~) ,000(y~) ,679(yx) -,001(y~) -,256(yx) ,002(y~) ,004(y~) ,005(y~) ,004(y~) ,004(y~) ,000(y~) -,001(y~)
D -,434(~x) ,000(~y) ,016(~~) ,019 ,006 ,014 ,016 ,019 -,024 -,030 -,021 -,016 1,903(~x) -,009 -,533(~x) -,016 -,029 -,037 -,045 -,032 ,005 ,019
DL -,185(~x) -,001(~y) ,019 ,023(~~) ,006 ,017 ,018 ,020 -,031 -,039 -,026 -,018 1,907(~x) -,010 -,803(~x) -,019 -,036 -,047 -,058 -,044 ,005 ,023
D2H -,199(~x) ,001(~y) ,006 ,006 ,003(~~) ,005 ,007 ,008 -,007 -,009 -,006 -,006 ,668(~x) -,004 ,517(~x) -,006 -,009 -,011 -,014 -,009 ,002 ,006
D2HL ,288(~x) -,001(~y) ,014 ,017 ,005 ,013(~~) ,013 ,015 -,023 -,029 -,019 -,013 1,179(~x) -,007 -,511(~x) -,014 -,026 -,035 -,042 -,032 ,004 ,017
DSQ -,510(~x) ,001(~y) ,016 ,018 ,007 ,013 ,017(~~) ,021 -,022 -,027 -,019 -,017 1,461(~x) -,010 -,007(~x) -,016 -,027 -,034 -,041 -,028 ,005 ,018
DCU -,387(~x) ,002(~y) ,019 ,020 ,008 ,015 ,021 ,027(~~) -,025 -,030 -,022 -,021 ,605(~x) -,012 ,717(~x) -,019 -,031 -,038 -,046 -,031 ,005 ,020
DR -,174(~x) ,002(~y) -,024 -,031 -,007 -,023 -,022 -,025 ,041(~~) ,053 ,035 ,022 -1,567(~x) ,012 ,843(~x) ,025 ,047 ,063 ,077 ,059 -,007 -,031
D2R -,577(~x) ,004(~y) -,030 -,039 -,009 -,029 -,027 -,030 ,053 ,069(~~) ,044 ,028 -1,015(~x) ,015 ,718(~x) ,032 ,061 ,082 ,098 ,077 -,009 -,039
DL2 ,046(~x) ,002(~y) -,021 -,026 -,006 -,019 -,019 -,022 ,035 ,044 ,029(~~) ,019 -1,819(~x) ,011 ,865(~x) ,021 ,040 ,052 ,065 ,050 -,006 -,026
H2 ,573(~x) ,000(~y) -,016 -,018 -,006 -,013 -,017 -,021 ,022 ,028 ,019 ,017(~~) ,327(~x) ,009 ,118(~x) ,016 ,027 ,035 ,041 ,028 -,005 -,018
DH -85,855 -,679(xy) -1,903(x~) -1,907(x~) -,668(x~) -1,179(x~) -1,461(x~) -,605(x~) 1,567(x~) 1,015(x~) 1,819(x~) -,327(x~) 174,433(xx) -,541(x~) -97,607 -,734(x~) -,288(x~) -,554(x~) 6,885(x~) 4,232(x~) ,184(x~) -1,907(x~)
DH2 ,087(~x) -,001(~y) -,009 -,010 -,004 -,007 -,010 -,012 ,012 ,015 ,011 ,009 ,541(~x) ,005(~~) ,389(~x) ,009 ,015 ,018 ,023 ,015 -,002 -,010
D2H2 45,859 ,256(xy) ,533(x~) ,803(x~) -,517(x~) ,511(x~) ,007(x~) -,717(x~) -,843(x~) -,718(x~) -,865(x~) -,118(x~) -97,607 -,389(x~) 57,356(xx) ,180(x~) -,104(x~) -,045(x~) -2,804(x~) -2,033(x~) -,035(x~) ,803(x~)
HR -1,524(~x) ,002(~y) -,016 -,019 -,006 -,014 -,016 -,019 ,025 ,032 ,021 ,016 ,734(~x) ,009 -,180(~x) ,019(~~) ,032 ,042 ,045 ,031 -,005 -,019
DHR -1,310(~x) ,004(~y) -,029 -,036 -,009 -,026 -,027 -,031 ,047 ,061 ,040 ,027 ,288(~x) ,015 ,104(~x) ,032 ,059(~~) ,077 ,087 ,064 -,009 -,036
D2HR -1,478(~x) ,005(~y) -,037 -,047 -,011 -,035 -,034 -,038 ,063 ,082 ,052 ,035 ,554(~x) ,018 ,045(~x) ,042 ,077 ,103(~~) ,114 ,086 -,011 -,047
HDD 4,651(~x) ,004(~y) -,045 -,058 -,014 -,042 -,041 -,046 ,077 ,098 ,065 ,041 -6,885(~x) ,023 2,804(~x) ,045 ,087 ,114 ,145(~~) ,112 -,012 -,058
HDD2 1,474(~x) ,004(~y) -,032 -,044 -,009 -,032 -,028 -,031 ,059 ,077 ,050 ,028 -4,232(~x) ,015 2,033(~x) ,031 ,064 ,086 ,112 ,090(~~) -,009 -,044
HL 1,144(~x) ,000(~y) ,005 ,005 ,002 ,004 ,005 ,005 -,007 -,009 -,006 -,005 -,184(~x) -,002 ,035(~x) -,005 -,009 -,011 -,012 -,009 ,001(~~) ,005
D2L -,185(~x) -,001(~y) ,019 ,023 ,006 ,017 ,018 ,020 -,031 -,039 -,026 -,018 1,907(~x) -,010 -,803(~x) -,019 -,036 -,047 -,058 -,044 ,005 ,023(~~)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
x~ Row variable is an independent variable, column variable is an excluded independent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
y~ Row variable is the dependent variable, column variable is an excluded independent variable.
~x Row variable is an excluded independent variable, column variable is an independent variable.
~y Row variable is an excluded independent variable, column variable is the dependent variable.
~~ This variable is an excluded predictor.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) HL2 DH D2H2
1 1 1,986 1,000 ,01 ,01

2 1,381E-02 11,994 ,99 ,99

2 1 2,913 1,000 ,00 ,00 ,00
2 8,514E-02 5,849 ,04 ,00 ,13
3 2,125E-03 37,024 ,96 1,00 ,87
3 1 3,640 1,000 ,00 ,00 ,00 ,00
2 ,348 3,233 ,00 ,00 ,00 ,02
3 1,136E-02 17,900 ,10 ,01 ,03 ,11
4 3,253E-04 105,776 ,89 ,99 ,97 ,87
a Dependent Variable: FH

EQUATION 3

Regression

Notes
Output Created 19-OCT-2004 09:31:30
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fHl D Dl D2H TO D2l/ STATISTICS = all/
DEPENDENT = fHl/ METHOD = STEPWISE.
Resources Memory Required 12980 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,04

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(a)
Model Variables Entered Variables Removed Method
1 HL , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
2 DL2 , Stepwise (Criteria: Probability-of-F-to-enter <= ,050, Probability-of-F-to-remove >= ,100).
a Dependent Variable: FHL





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,978(a) ,956 ,956 4,631E-02 ,956 7643,072 1 348 ,000 -2148,720 ,044 29,934 -2141,004(b)
2 ,979(c) ,958 ,958 4,547E-02 ,002 13,871 1 347 ,000 -2160,439 ,043 17,484 -2148,865(b)
a Predictors: (Constant), HL
b Multicollinearity is present. The following variables were not included in the full model used for calculation of the Mallows' Prediction Criterion: D, DL, D2H, D2HL, DSQ, DR, D2R, DL2, DH, DH2, HR, DHR, HL, HL2
c Predictors: (Constant), HL, DL2

ANOVA(c)
Model Sum of Squares df Mean Square F Sig.
1 Regression 16,390 1 16,390 7643,072 ,000(a)
Residual ,746 348 2,144E-03

Total 17,136 349


2 Regression 16,418 2 8,209 3969,817 ,000(b)
Residual ,718 347 2,068E-03

Total 17,136 349


a Predictors: (Constant), HL
b Predictors: (Constant), HL, DL2
c Dependent Variable: FHL



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) -,788 ,029

-27,088 ,000 -,845 -,731




HL ,986 ,011 ,978 ,011 87,425 ,000 ,964 1,009 ,978 ,978 ,978 1,000 1,000
2 (Constant) -,149 ,174

-,857 ,392 -,491 ,193




HL ,823 ,045 ,816 ,045 18,171 ,000 ,734 ,912 ,978 ,698 ,200 ,060 16,705
DL2 -4,033E-02 ,011 -,167 ,045 -3,724 ,000 -,062 -,019 -,958 -,196 -,041 ,060 16,705
a Dependent Variable: FHL





Excluded Variables(c)

Beta In t Sig. Partial Correlation Collinearity Statistics
Model Tolerance VIF Minimum Tolerance
1 D ,074(a) 2,683 ,008 ,143 ,163 6,142 ,163
DL ,135(a) 3,442 ,001 ,182 7,930E-02 12,611 7,930E-02
D2H ,025(a) 1,308 ,192 ,070 ,333 3,007 ,333
D2HL ,206(a) 3,442 ,001 ,182 3,377E-02 29,608 3,377E-02
DSQ ,043(a) 2,135 ,033 ,114 ,301 3,324 ,301
DCU ,029(a) 1,798 ,073 ,096 ,470 2,128 ,470
DR -,180(a) -3,683 ,000 -,194 5,041E-02 19,837 5,041E-02
D2R -,113(a) -2,590 ,010 -,138 6,426E-02 15,561 6,426E-02
DL2 -,167(a) -3,724 ,000 -,196 5,986E-02 16,705 5,986E-02
H2 -,021(a) -,528 ,598 -,028 7,757E-02 12,892 7,757E-02
DH ,038(a) 1,313 ,190 ,070 ,151 6,626 ,151
DH2 ,011(a) ,451 ,652 ,024 ,221 4,532 ,221
D2H2 ,013(a) ,722 ,471 ,039 ,406 2,461 ,406
HR ,028(a) ,368 ,713 ,020 2,157E-02 46,365 2,157E-02
DHR -,042(a) -,900 ,369 -,048 5,760E-02 17,362 5,760E-02
D2HR -,018(a) -,537 ,592 -,029 ,115 8,710 ,115
HDD -,041(a) -3,355 ,001 -,177 ,800 1,250 ,800
HDD2 -,079(a) -3,553 ,000 -,187 ,244 4,101 ,244
HL2 ,015(a) ,077 ,939 ,004 3,313E-03 301,797 3,313E-03
D2L ,135(a) 3,442 ,001 ,182 7,930E-02 12,611 7,930E-02
2 D -,043(b) -,843 ,400 -,045 4,590E-02 21,785 1,688E-02
DL -,135(b) -,782 ,435 -,042 4,043E-03 247,369 3,052E-03
D2H -,029(b) -1,211 ,227 -,065 ,207 4,824 3,731E-02
D2HL -,207(b) -,782 ,435 -,042 1,722E-03 580,783 1,722E-03
DSQ -,026(b) -,872 ,384 -,047 ,137 7,317 2,720E-02
DCU -,018(b) -,838 ,403 -,045 ,266 3,764 3,385E-02
DR -,076(b) -,520 ,604 -,028 5,599E-03 178,613 5,599E-03
D2R -,021(b) -,374 ,709 -,020 3,925E-02 25,477 3,656E-02
H2 -,060(b) -1,478 ,140 -,079 7,311E-02 13,679 4,287E-02
DH -,046(b) -1,265 ,207 -,068 9,216E-02 10,850 3,656E-02
DH2 -,042(b) -1,572 ,117 -,084 ,168 5,969 4,546E-02
D2H2 -,030(b) -1,465 ,144 -,078 ,292 3,424 4,302E-02
HR -,034(b) -,441 ,659 -,024 2,056E-02 48,649 1,295E-02
DHR -,014(b) -,298 ,766 -,016 5,599E-02 17,861 3,512E-02
D2HR -,004(b) -,121 ,903 -,007 ,113 8,825 4,510E-02
HDD ,085(b) 1,393 ,165 ,075 3,253E-02 30,736 2,046E-03
HDD2 ,110(b) ,768 ,443 ,041 5,933E-03 168,551 1,457E-03
HL2 -,153(b) -,782 ,435 -,042 3,145E-03 317,993 3,145E-03
D2L -,135(b) -,782 ,435 -,042 4,043E-03 247,369 3,052E-03
a Predictors in the Model: (Constant), HL
b Predictors in the Model: (Constant), HL, DL2
c Dependent Variable: FHL

Coefficient Correlations(a)
Model HL DL2
1 Correlations HL 1,000
Covariances HL 1,273E-04
2 Correlations HL 1,000 ,970
DL2 ,970 1,000
Covariances HL 2,050E-03 4,755E-04
DL2 4,755E-04 1,173E-04
a Dependent Variable: FHL

Swept Correlation Matrix(a)

Columns
Model Rows HL FHL D DL D2H D2HL DSQ DCU DR D2R DL2 H2 DH DH2 D2H2 HR DHR D2HR HDD HDD2 HL2 D2L
1 HL 1,000(xx) -,978(xy) -,915(x~) -,960(x~) -,817(x~) -,983(x~) -,836(x~) -,728(x~) ,974(x~) ,967(x~) ,970(x~) -,960(x~) -,921(x~) -,883(x~) -,770(x~) ,989(x~) ,971(x~) ,941(x~) -,447(x~) ,870(x~) -,998(x~) -,960(x~)
FHL ,978(yx) ,044(yy) ,012(y~) ,011(y~) ,008(y~) ,007(y~) ,013(y~) ,014(y~) -,009(y~) -,007(y~) -,010(y~) -,002(y~) ,006(y~) ,002(y~) ,005(y~) ,001(y~) -,002(y~) -,002(y~) -,033(y~) -,019(y~) ,000(y~) ,011(y~)
D ,915(~x) ,012(~y) ,163(~~) ,107 ,217 ,070 ,217 ,261 -,057 -,015 -,084 ,071 ,146 ,163 ,228 ,034 ,027 ,045 -,337 -,160 ,014 ,107
DL ,960(~x) ,011(~y) ,107 ,079(~~) ,125 ,052 ,134 ,155 -,053 -,031 -,067 ,033 ,085 ,088 ,126 ,016 ,002 ,008 -,252 -,132 ,007 ,079
D2H ,817(~x) ,008(~y) ,217 ,125 ,333(~~) ,082 ,310 ,390 -,044 ,022 -,087 ,126 ,221 ,262 ,365 ,058 ,068 ,101 -,388 -,158 ,024 ,125
D2HL ,983(~x) ,007(~y) ,070 ,052 ,082 ,034(~~) ,087 ,101 -,035 -,021 -,044 ,022 ,056 ,058 ,082 ,010 ,001 ,005 -,164 -,086 ,004 ,052
DSQ ,836(~x) ,013(~y) ,217 ,134 ,310 ,087 ,301(~~) ,372 -,061 -,001 -,099 ,105 ,205 ,235 ,333 ,048 ,048 ,075 -,418 -,183 ,020 ,134
DCU ,728(~x) ,014(~y) ,261 ,155 ,390 ,101 ,372 ,470(~~) -,064 ,009 -,111 ,129 ,253 ,293 ,423 ,058 ,061 ,094 -,479 -,198 ,024 ,155
DR -,974(~x) -,009(~y) -,057 -,053 -,044 -,035 -,061 -,064 ,050(~~) ,048 ,052 ,004 -,030 -,020 -,036 ,003 ,025 ,032 ,172 ,105 ,001 -,053
D2R -,967(~x) -,007(~y) -,015 -,031 ,022 -,021 -,001 ,009 ,048 ,064(~~) ,039 ,038 ,018 ,037 ,037 ,021 ,051 ,070 ,105 ,080 ,008 -,031
DL2 -,970(~x) -,010(~y) -,084 -,067 -,087 -,044 -,099 -,111 ,052 ,039 ,060(~~) -,016 -,059 -,056 -,083 -,008 ,010 ,009 ,214 ,119 -,003 -,067
H2 ,960(~x) -,002(~y) ,071 ,033 ,126 ,022 ,105 ,129 ,004 ,038 -,016 ,078(~~) ,093 ,120 ,146 ,039 ,057 ,080 -,101 -,035 ,016 ,033
DH ,921(~x) ,006(~y) ,146 ,085 ,221 ,056 ,205 ,253 -,030 ,018 -,059 ,093 ,151(~~) ,180 ,242 ,044 ,053 ,078 -,265 -,112 ,018 ,085
DH2 ,883(~x) ,002(~y) ,163 ,088 ,262 ,058 ,235 ,293 -,020 ,037 -,056 ,120 ,180 ,221(~~) ,293 ,057 ,074 ,107 -,272 -,106 ,023 ,088
D2H2 ,770(~x) ,005(~y) ,228 ,126 ,365 ,082 ,333 ,423 -,036 ,037 -,083 ,146 ,242 ,293 ,406(~~) ,066 ,083 ,120 -,387 -,150 ,028 ,126
HR -,989(~x) ,001(~y) ,034 ,016 ,058 ,010 ,048 ,058 ,003 ,021 -,008 ,039 ,044 ,057 ,066 ,022(~~) ,032 ,046 -,048 -,018 ,008 ,016
DHR -,971(~x) -,002(~y) ,027 ,002 ,068 ,001 ,048 ,061 ,025 ,051 ,010 ,057 ,053 ,074 ,083 ,032 ,058(~~) ,081 -,001 ,018 ,013 ,002
D2HR -,941(~x) -,002(~y) ,045 ,008 ,101 ,005 ,075 ,094 ,032 ,070 ,009 ,080 ,078 ,107 ,120 ,046 ,081 ,115(~~) -,017 ,017 ,018 ,008
HDD ,447(~x) -,033(~y) -,337 -,252 -,388 -,164 -,418 -,479 ,172 ,105 ,214 -,101 -,265 -,272 -,387 -,048 -,001 -,017 ,800(~~) ,422 -,020 -,252
HDD2 -,870(~x) -,019(~y) -,160 -,132 -,158 -,086 -,183 -,198 ,105 ,080 ,119 -,035 -,112 -,106 -,150 -,018 ,018 ,017 ,422 ,244(~~) -,007 -,132
HL2 ,998(~x) ,000(~y) ,014 ,007 ,024 ,004 ,020 ,024 ,001 ,008 -,003 ,016 ,018 ,023 ,028 ,008 ,013 ,018 -,020 -,007 ,003(~~) ,007
D2L ,960(~x) ,011(~y) ,107 ,079 ,125 ,052 ,134 ,155 -,053 -,031 -,067 ,033 ,085 ,088 ,126 ,016 ,002 ,008 -,252 -,132 ,007 ,079(~~)
2 HL 16,705(xx) -,816(xy) ,440(x~) ,128(x~) ,586(x~) -,273(x~) ,769(x~) 1,062(x~) ,136(x~) ,341(x~) 16,197 -,696(x~) ,039(x~) ,030(x~) ,570(x~) 1,115(x~) ,812(x~) ,787(x~) -3,919(x~) -1,063(x~) -,947(x~) ,128(x~)
FHL ,816(yx) ,042(yy) -,002(y~) -,001(y~) -,006(y~) ,000(y~) -,004(y~) -,005(y~) ,000(y~) -,001(y~) -,167(yx) -,004(y~) -,004(y~) -,007(y~) -,009(y~) -,001(y~) -,001(y~) ,000(y~) ,003(y~) ,001(y~) ,000(y~) -,001(y~)
D -,440(~x) -,002(~y) ,046(~~) ,014 ,096 ,009 ,079 ,106 ,015 ,039 -1,397(~x) ,048 ,064 ,084 ,113 ,023 ,041 ,058 -,038 ,007 ,009 ,014
DL -,128(~x) -,001(~y) ,014 ,004(~~) ,028 ,003 ,023 ,031 ,005 ,012 -1,121(~x) ,015 ,019 ,025 ,033 ,007 ,013 ,018 -,011 ,002 ,003 ,004
D2H -,586(~x) -,006(~y) ,096 ,028 ,207(~~) ,018 ,167 ,230 ,031 ,078 -1,447(~x) ,103 ,135 ,180 ,245 ,047 ,082 ,115 -,078 ,014 ,019 ,028
D2HL ,273(~x) ,000(~y) ,009 ,003 ,018 ,002(~~) ,015 ,020 ,003 ,008 -,732(~x) ,010 ,012 ,016 ,021 ,005 ,008 ,012 -,007 ,001 ,002 ,003
DSQ -,769(~x) -,004(~y) ,079 ,023 ,167 ,015 ,137(~~) ,189 ,025 ,063 -1,656(~x) ,078 ,107 ,141 ,196 ,035 ,064 ,090 -,063 ,014 ,015 ,023
DCU -1,062(~x) -,005(~y) ,106 ,031 ,230 ,020 ,189 ,266(~~) ,032 ,080 -1,847(~x) ,099 ,143 ,189 ,270 ,043 ,079 ,111 -,083 ,022 ,018 ,031
DR -,136(~x) ,000(~y) ,015 ,005 ,031 ,003 ,025 ,032 ,006(~~) ,015 ,865(~x) ,018 ,022 ,029 ,036 ,010 ,017 ,024 -,013 ,001 ,004 ,005
D2R -,341(~x) -,001(~y) ,039 ,012 ,078 ,008 ,063 ,080 ,015 ,039(~~) ,646(~x) ,049 ,056 ,074 ,091 ,026 ,045 ,064 -,034 ,003 ,010 ,012
DL2 16,197 ,167(xy) 1,397(x~) 1,121(x~) 1,447(x~) ,732(x~) 1,656(x~) 1,847(x~) -,865(x~) -,646(x~) 16,705(xx) ,273(x~) ,991(x~) ,942(x~) 1,382(x~) ,130(x~) -,164(x~) -,159(x~) -3,581(x~) -1,993(x~) ,053(x~) 1,121(x~)
H2 ,696(~x) -,004(~y) ,048 ,015 ,103 ,010 ,078 ,099 ,018 ,049 -,273(~x) ,073(~~) ,076 ,105 ,124 ,037 ,060 ,083 -,042 -,002 ,015 ,015
DH -,039(~x) -,004(~y) ,064 ,019 ,135 ,012 ,107 ,143 ,022 ,056 -,991(~x) ,076 ,092(~~) ,124 ,160 ,037 ,063 ,088 -,053 ,006 ,015 ,019
DH2 -,030(~x) -,007(~y) ,084 ,025 ,180 ,016 ,141 ,189 ,029 ,074 -,942(~x) ,105 ,124 ,168(~~) ,215 ,049 ,083 ,116 -,070 ,006 ,020 ,025
D2H2 -,570(~x) -,009(~y) ,113 ,033 ,245 ,021 ,196 ,270 ,036 ,091 -1,382(~x) ,124 ,160 ,215 ,292(~~) ,055 ,096 ,134 -,091 ,015 ,023 ,033
HR -1,115(~x) -,001(~y) ,023 ,007 ,047 ,005 ,035 ,043 ,010 ,026 -,130(~x) ,037 ,037 ,049 ,055 ,021(~~) ,034 ,047 -,020 -,002 ,008 ,007
DHR -,812(~x) -,001(~y) ,041 ,013 ,082 ,008 ,064 ,079 ,017 ,045 ,164(~x) ,060 ,063 ,083 ,096 ,034 ,056(~~) ,079 -,036 -,002 ,013 ,013
D2HR -,787(~x) ,000(~y) ,058 ,018 ,115 ,012 ,090 ,111 ,024 ,064 ,159(~x) ,083 ,088 ,116 ,134 ,047 ,079 ,113(~~) -,051 -,002 ,018 ,018
HDD 3,919(~x) ,003(~y) -,038 -,011 -,078 -,007 -,063 -,083 -,013 -,034 3,581(~x) -,042 -,053 -,070 -,091 -,020 -,036 -,051 ,033(~~) -,005 -,008 -,011
HDD2 1,063(~x) ,001(~y) ,007 ,002 ,014 ,001 ,014 ,022 ,001 ,003 1,993(~x) -,002 ,006 ,006 ,015 -,002 -,002 -,002 -,005 ,006(~~) -,001 ,002
HL2 ,947(~x) ,000(~y) ,009 ,003 ,019 ,002 ,015 ,018 ,004 ,010 -,053(~x) ,015 ,015 ,020 ,023 ,008 ,013 ,018 -,008 -,001 ,003(~~) ,003
D2L -,128(~x) -,001(~y) ,014 ,004 ,028 ,003 ,023 ,031 ,005 ,012 -1,121(~x) ,015 ,019 ,025 ,033 ,007 ,013 ,018 -,011 ,002 ,003 ,004(~~)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
x~ Row variable is an independent variable, column variable is an excluded independent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
y~ Row variable is the dependent variable, column variable is an excluded independent variable.
~x Row variable is an excluded independent variable, column variable is an independent variable.
~y Row variable is an excluded independent variable, column variable is the dependent variable.
~~ This variable is an excluded predictor.
a Dependent Variable: FHL



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) HL DL2
1 1 1,996 1,000 ,00 ,00
2 3,629E-03 23,455 1,00 1,00
2 1 2,967 1,000 ,00 ,00 ,00
2 3,248E-02 9,558 ,00 ,01 ,03
3 1,251E-04 153,993 1,00 ,99 ,97
a Dependent Variable: FHL

EQUATION 4

Regression

Notes
Output Created 19-OCT-2004 09:31:30
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D Dsq Dcu/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER D Dsq Dcu.
Resources Memory Required 2004 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:04,29

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DCU, D, DSQ(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,958(a) ,917 ,916 ,369277 ,917 1277,828 3 346 ,000 -693,368 ,085 4,000 -677,936
a Predictors: (Constant), DCU, D, DSQ

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 522,756 3 174,252 1277,828 ,000(a)
Residual 47,183 346 ,136

Total 569,938 349


a Predictors: (Constant), DCU, D, DSQ
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) -3,873 ,888

-4,360 ,000 -5,620 -2,126




D 135,430 22,901 2,268 ,384 5,914 ,000 90,387 180,473 ,932 ,303 ,091 ,002 614,721
DSQ -391,501 188,045 -1,530 ,735 -2,082 ,038 -761,355 -21,647 ,873 -,111 -,032 ,000 2256,353
DCU 236,412 487,239 ,179 ,369 ,485 ,628 -721,911 1194,734 ,782 ,026 ,008 ,002 570,212
a Dependent Variable: FH

Coefficient Correlations(a)
Model DCU D DSQ
1 Correlations DCU 1,000 ,977 -,994
D ,977 1,000 -,994
DSQ -,994 -,994 1,000
Covariances DCU 237401,579 10899,309 -91048,093
D 10899,309 524,463 -4281,394
DSQ -91048,093 -4281,394 35360,763
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows DCU D DSQ FH
1 DCU 570,212(xx) 578,305 -1127,172 -,179(xy)
D 578,305 614,721(xx) -1170,873 -2,268(xy)
DSQ -1127,172 -1170,873 2256,353(xx) 1,530(xy)
FH ,179(yx) 2,268(yx) -1,530(yx) ,083(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) D DSQ DCU
1 1 3,732 1,000 ,00 ,00 ,00 ,00
2 ,262 3,777 ,00 ,00 ,00 ,00
3 6,185E-03 24,564 ,02 ,00 ,00 ,03
4 3,367E-05 332,946 ,98 1,00 1,00 ,97
a Dependent Variable: FH

EQUATION 5

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D Dsq/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER D Dsq.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DSQ, D(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,958(a) ,917 ,917 ,368870 ,917 1920,856 2 347 ,000 -695,130 ,084 3,000 -683,556
a Predictors: (Constant), DSQ, D

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 522,724 2 261,362 1920,856 ,000(a)
Residual 47,215 347 ,136

Total 569,938 349


a Predictors: (Constant), DSQ, D
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) -3,464 ,278

-12,441 ,000 -4,011 -2,916




D 124,576 4,900 2,086 ,082 25,422 ,000 114,938 134,214 ,932 ,807 ,393 ,035 28,208
DSQ -300,832 21,002 -1,175 ,082 -14,324 ,000 -342,140 -259,525 ,873 -,610 -,221 ,035 28,208
a Dependent Variable: FH

Coefficient Correlations(a)
Model DSQ D
1 Correlations DSQ 1,000 -,982
D -,982 1,000
Covariances DSQ 441,086 -101,076
D -101,076 24,013
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows DSQ D FH
1 DSQ 28,208(xx) -27,703 1,175(xy)
D -27,703 28,208(xx) -2,086(xy)
FH -1,175(yx) 2,086(yx) ,083(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) D DSQ
1 1 2,902 1,000 ,00 ,00 ,00
2 9,655E-02 5,483 ,02 ,00 ,04
3 1,008E-03 53,659 ,97 1,00 ,96
a Dependent Variable: FH

EQUATION 6

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D Dsq/ ORIGIN/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER D Dsq.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b,c)
Model Variables Entered Variables Removed Method
1 DSQ, D(a) , Enter
a All requested variables entered.
b Dependent Variable: FH
c Linear Regression through the Origin





Model Summary

R R Square(a) Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,997(b) ,995 ,995 ,442930 ,995 31990,870 2 348 ,000 -568,045 ,005 2,000 -560,330
a For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models which include an intercept.
b Predictors: DSQ, D

ANOVA(c,d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 12552,411 2 6276,206 31990,870 ,000(a)
Residual 68,273 348 ,196

Total 12620,684(b) 350


a Predictors: DSQ, D
b This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.
c Dependent Variable: FH
d Linear Regression through the Origin



Coefficients(a,b)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 D 64,452 ,973 1,101 ,017 66,257 ,000 62,539 66,365 ,997 ,963 ,261 ,056 17,755
DSQ -55,108 8,571 -,107 ,017 -6,430 ,000 -71,965 -38,250 ,962 -,326 -,025 ,056 17,755
a Dependent Variable: FH
b Linear Regression through the Origin

Coefficient Correlations(a,b)
Model DSQ D
1 Correlations DSQ 1,000 -,971
D -,971 1,000
Covariances DSQ 73,462 -8,099
D -8,099 ,946
a Dependent Variable: FH
b Linear Regression through the Origin

Swept Correlation Matrix(a,b)

Columns
Model Rows DSQ D FH
1 DSQ 17,755(xx) -17,248 ,107(xy)
D -17,248 17,755(xx) -1,101(xy)
FH -,107(yx) 1,101(yx) ,005(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH
b Linear Regression through the Origin



Collinearity Diagnostics(a,b)

Eigenvalue Condition Index Variance Proportions
Model Dimension D DSQ
1 1 1,971 1,000 ,01 ,01
2 2,857E-02 8,307 ,99 ,99
a Dependent Variable: FH
b Linear Regression through the Origin

EQUATION 7

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH Dsq/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER Dsq.
Resources Memory Required 1564 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DSQ(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,873(a) ,763 ,762 ,623190 ,763 1119,531 1 348 ,000 -329,039 ,240 2,000 -321,323
a Predictors: (Constant), DSQ

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 434,787 1 434,787 1119,531 ,000(a)
Residual 135,151 348 ,388

Total 569,938 349


a Predictors: (Constant), DSQ
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) 3,517 ,078

45,226 ,000 3,364 3,670




DSQ 223,534 6,681 ,873 ,026 33,459 ,000 210,394 236,673 ,873 ,873 ,873 1,000 1,000
a Dependent Variable: FH

Coefficient Correlations(a)
Model DSQ
1 Correlations DSQ 1,000
Covariances DSQ 44,632
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows DSQ FH
1 DSQ 1,000(xx) -,873(xy)
FH ,873(yx) ,237(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) DSQ
1 1 1,904 1,000 ,05 ,05
2 9,640E-02 4,444 ,95 ,95
a Dependent Variable: FH

EQUATION 8

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER D.
Resources Memory Required 1564 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 D(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,932(a) ,868 ,868 ,464647 ,868 2291,869 1 348 ,000 -534,540 ,133 2,000 -526,825
a Predictors: (Constant), D

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 494,806 1 494,806 2291,869 ,000(a)
Residual 75,132 348 ,216

Total 569,938 349


a Predictors: (Constant), D
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) ,287 ,119

2,408 ,017 ,053 ,521




D 55,640 1,162 ,932 ,019 47,873 ,000 53,354 57,925 ,932 ,932 ,932 1,000 1,000
a Dependent Variable: FH

Coefficient Correlations(a)
Model D
1 Correlations D 1,000
Covariances D 1,351
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows D FH
1 D 1,000(xx) -,932(xy)
FH ,932(yx) ,132(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) D
1 1 1,978 1,000 ,01 ,01
2 2,195E-02 9,493 ,99 ,99
a Dependent Variable: FH

EQUATION 9

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D/ ORIGIN/ STATISTICS = all/ DEPENDENT fH/
METROD = ENTER D.
Resources Memory Required 1564 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b,c)
Model Variables Entered Variables Removed Method
1 D(a) , Enter
a All requested variables entered.
b Dependent Variable: FH
c Linear Regression through the Origin





Model Summary

R R Square(a) Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,997(b) ,994 ,994 ,467829 ,994 57315,561 1 349 ,000 -530,758 ,006 1,000 -526,900
a For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models which include an intercept.
b Predictors: D

ANOVA(c,d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 12544,301 1 12544,301 57315,561 ,000(a)
Residual 76,383 349 ,219

Total 12620,684(b) 350


a Predictors: D
b This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.
c Dependent Variable: FH
d Linear Regression through the Origin



Coefficients(a,b)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 D 58,376 ,244 ,997 ,004 239,407 ,000 57,897 58,856 ,997 ,997 ,997 1,000 1,000
a Dependent Variable: FH
b Linear Regression through the Origin

Coefficient Correlations(a,b)
Model D
1 Correlations D 1,000
Covariances D 5,946E-02
a Dependent Variable: FH
b Linear Regression through the Origin

Swept Correlation Matrix(a,b)

Columns
Model Rows D FH
1 D 1,000(xx) -,997(xy)
FH ,997(yx) ,006(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH
b Linear Regression through the Origin



Collinearity Diagnostics(a,b)

Eigenvalue Condition Index Variance Proportions
Model Dimension D
1 1 1,000 1,000 1,00
a Dependent Variable: FH
b Linear Regression through the Origin

EQUATION 10

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH Dr D2r/ STATISTICS = all/
DEPENDENT = fH/ METHOD ENTER = Dr D2r.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 D2R, DR(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,957(a) ,916 ,916 ,370949 ,916 1897,446 2 347 ,000 -691,196 ,085 3,000 -679,622
a Predictors: (Constant), D2R, DR

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 522,190 2 261,095 1897,446 ,000(a)
Residual 47,748 347 ,138

Total 569,938 349


a Predictors: (Constant), D2R, DR
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) 15,040 ,383

39,274 ,000 14,287 15,793




DR -1,177 ,072 -1,875 ,115 -16,250 ,000 -1,320 -1,035 -,949 -,657 -,252 ,018 55,114
D2R 2,724E-02 ,003 ,934 ,115 8,098 ,000 ,021 ,034 -,923 ,399 ,126 ,018 55,114
a Dependent Variable: FH

Coefficient Correlations(a)
Model D2R DR
1 Correlations D2R 1,000 -,991
DR -,991 1,000
Covariances D2R 1,132E-05 -2,415E-04
DR -2,415E-04 5,248E-03
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows D2R DR FH
1 D2R 55,114(xx) -54,612 -,934(xy)
DR -54,612 55,114(xx) 1,875(xy)
FH ,934(yx) -1,875(yx) ,084(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) DR D2R
1 1 2,931 1,000 ,00 ,00 ,00
2 6,871E-02 6,531 ,02 ,00 ,02
3 4,411E-04 81,512 ,98 1,00 ,98
a Dependent Variable: FH

EQUATION 11

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH Dl/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER Dl.
Resources Memory Required 1564 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DL(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,955(a) ,911 ,911 ,381087 ,911 3576,459 1 348 ,000 -673,315 ,090 2,000 -665,599
a Predictors: (Constant), DL

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 519,399 1 519,399 3576,459 ,000(a)
Residual 50,539 348 ,145

Total 569,938 349


a Predictors: (Constant), DL
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) 19,953 ,236

84,402 ,000 19,488 20,418




DL 6,070 ,102 ,955 ,016 59,804 ,000 5,871 6,270 ,955 ,955 ,955 1,000 1,000
a Dependent Variable: FH

Coefficient Correlations(a)
Model DL
1 Correlations DL 1,000
Covariances DL 1,030E-02
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows DL FH
1 DL 1,000(xx) -,955(xy)
FH ,955(yx) ,089(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) DL
1 1 1,996 1,000 ,00 ,00
2 3,719E-03 23,168 1,00 1,00
a Dependent Variable: FH

EQUATION 12

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH D Dl/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER D Dl.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DL, D(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,956(a) ,914 ,914 ,375808 ,914 1844,241 2 347 ,000 -682,086 ,087 3,000 -670,513
a Predictors: (Constant), DL, D

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 520,931 2 260,465 1844,241 ,000(a)
Residual 49,007 347 ,141

Total 569,938 349


a Predictors: (Constant), DL, D
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) 26,185 1,907

13,734 ,000 22,435 29,935




D -18,128 5,505 -,304 ,092 -3,293 ,001 -28,955 -7,301 ,932 -,174 -,052 ,029 34,293
DL 7,972 ,586 1,254 ,092 13,601 ,000 6,820 9,125 ,955 ,590 ,214 ,029 34,293
a Dependent Variable: FH

Coefficient Correlations(a)
Model DL D
1 Correlations DL 1,000 -,985
D -,985 1,000
Covariances DL ,344 -3,179
D -3,179 30,302
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows DL D FH
1 DL 34,293(xx) -33,789 -1,254(xy)
D -33,789 34,293(xx) ,304(xy)
FH 1,254(yx) -,304(yx) ,086(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) D DL
1 1 2,954 1,000 ,00 ,00 ,00
2 4,581E-02 8,030 ,00 ,02 ,00
3 6,947E-05 206,214 1,00 ,98 1,00
a Dependent Variable: FH

EQUATION 13

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH H H2/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER H H2.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 H2, H(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,974(a) ,948 ,948 ,292746 ,948 3151,696 2 347 ,000 -856,929 ,053 3,000 -845,355
a Predictors: (Constant), H2, H

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 540,201 2 270,100 3151,696 ,000(a)
Residual 29,738 347 8,570E-02

Total 569,938 349


a Predictors: (Constant), H2, H
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) -,345 ,266

-1,294 ,196 -,869 ,179




H ,498 ,039 1,121 ,088 12,720 ,000 ,421 ,575 ,973 ,564 ,156 ,019 51,637
H2 -2,378E-03 ,001 -,149 ,088 -1,690 ,092 -,005 ,000 ,961 -,090 -,021 ,019 51,637
a Dependent Variable: FH

Coefficient Correlations(a)
Model H2 H
1 Correlations H2 1,000 -,990
H -,990 1,000
Covariances H2 1,979E-06 -5,459E-05
H -5,459E-05 1,535E-03
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows H2 H FH
1 H2 51,637(xx) -51,135 ,149(xy)
H -51,135 51,637(xx) -1,121(xy)
FH -,149(yx) 1,121(yx) ,052(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) H H2
1 1 2,919 1,000 ,00 ,00 ,00
2 8,083E-02 6,009 ,02 ,00 ,02
3 5,618E-04 72,076 ,98 1,00 ,98
a Dependent Variable: FH

EQUATION 14

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH H H2/ ORIGIN/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER H H2.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b,c)
Model Variables Entered Variables Removed Method
1 H2, H(a) , Enter
a All requested variables entered.
b Dependent Variable: FH
c Linear Regression through the Origin





Model Summary

R R Square(a) Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,999(b) ,998 ,998 ,293029 ,998 73316,451 2 348 ,000 -857,244 ,002 2,000 -849,528
a For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models which include an intercept.
b Predictors: H2, H

ANOVA(c,d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 12590,803 2 6295,402 73316,451 ,000(a)
Residual 29,881 348 8,587E-02

Total 12620,684(b) 350


a Predictors: H2, H
b This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.
c Dependent Variable: FH
d Linear Regression through the Origin



Coefficients(a,b)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 H ,448 ,006 1,020 ,013 76,604 ,000 ,437 ,460 ,999 ,972 ,200 ,038 26,043
H2 -6,297E-04 ,000 -,021 ,013 -1,599 ,111 -,001 ,000 ,979 -,085 -,004 ,038 26,043
a Dependent Variable: FH
b Linear Regression through the Origin

Coefficient Correlations(a,b)
Model H2 H
1 Correlations H2 1,000 -,981
H -,981 1,000
Covariances H2 1,551E-07 -2,260E-06
H -2,260E-06 3,424E-05
a Dependent Variable: FH
b Linear Regression through the Origin

Swept Correlation Matrix(a,b)

Columns
Model Rows H2 H FH
1 H2 26,043(xx) -25,538 ,021(xy)
H -25,538 26,043(xx) -1,020(xy)
FH -,021(yx) 1,020(yx) ,002(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH
b Linear Regression through the Origin



Collinearity Diagnostics(a,b)

Eigenvalue Condition Index Variance Proportions
Model Dimension H H2
1 1 1,981 1,000 ,01 ,01
2 1,939E-02 10,107 ,99 ,99
a Dependent Variable: FH
b Linear Regression through the Origin

EQUATION 15

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH H/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER H.
Resources Memory Required 1564 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 H(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,973(a) ,947 ,947 ,293525 ,947 6267,103 1 348 ,000 -856,060 ,053 2,000 -848,344
a Predictors: (Constant), H

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 539,956 1 539,956 6267,103 ,000(a)
Residual 29,983 348 8,616E-02

Total 569,938 349


a Predictors: (Constant), H
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) 8,751E-02 ,075

1,172 ,242 -,059 ,234




H ,433 ,005 ,973 ,012 79,165 ,000 ,422 ,444 ,973 ,973 ,973 1,000 1,000
a Dependent Variable: FH

Coefficient Correlations(a)
Model H
1 Correlations H 1,000
Covariances H 2,989E-05
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows H FH
1 H 1,000(xx) -,973(xy)
FH ,973(yx) ,053(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) H
1 1 1,978 1,000 ,01 ,01
2 2,232E-02 9,414 ,99 ,99
a Dependent Variable: FH

EQUATION 16

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH H/ ORIGIN/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER H.
Resources Memory Required 1564 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b,c)
Model Variables Entered Variables Removed Method
1 H(a) , Enter
a All requested variables entered.
b Dependent Variable: FH
c Linear Regression through the Origin





Model Summary

R R Square(a) Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,999(b) ,998 ,998 ,293682 ,998 145979,113 1 349 ,000 -856,681 ,002 1,000 -852,824
a For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models which include an intercept.
b Predictors: H

ANOVA(c,d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 12590,583 1 12590,583 145979,113 ,000(a)
Residual 30,101 349 8,625E-02

Total 12620,684(b) 350


a Predictors: H
b This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.
c Dependent Variable: FH
d Linear Regression through the Origin



Coefficients(a,b)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 H ,439 ,001 ,999 ,003 382,072 ,000 ,437 ,441 ,999 ,999 ,999 1,000 1,000
a Dependent Variable: FH
b Linear Regression through the Origin

Coefficient Correlations(a,b)
Model H
1 Correlations H 1,000
Covariances H 1,321E-06
a Dependent Variable: FH
b Linear Regression through the Origin

Swept Correlation Matrix(a,b)

Columns
Model Rows H FH
1 H 1,000(xx) -,999(xy)
FH ,999(yx) ,002(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH
b Linear Regression through the Origin



Collinearity Diagnostics(a,b)

Eigenvalue Condition Index Variance Proportions
Model Dimension H
1 1 1,000 1,000 1,00
a Dependent Variable: FH
b Linear Regression through the Origin

EQUATION 17

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH H Dsq/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER H Dsq.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DSQ, H(a) , Enter
a All requested variables entered.
b Dependent Variable: FH





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,974(a) ,949 ,948 ,290356 ,949 3206,646 2 347 ,000 -862,665 ,052 3,000 -851,092
a Predictors: (Constant), DSQ, H

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 540,684 2 270,342 3206,646 ,000(a)
Residual 29,254 347 8,431E-02

Total 569,938 349


a Predictors: (Constant), DSQ, H
b Dependent Variable: FH



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) ,278 ,098

2,829 ,005 ,085 ,471




H ,403 ,011 ,907 ,026 35,441 ,000 ,381 ,426 ,973 ,885 ,431 ,226 4,429
DSQ 19,253 6,551 ,075 ,026 2,939 ,004 6,369 32,137 ,873 ,156 ,036 ,226 4,429
a Dependent Variable: FH

Coefficient Correlations(a)
Model DSQ H
1 Correlations DSQ 1,000 -,880
H -,880 1,000
Covariances DSQ 42,912 -6,561E-02
H -6,561E-02 1,296E-04
a Dependent Variable: FH

Swept Correlation Matrix(a)

Columns
Model Rows DSQ H FH
1 DSQ 4,429(xx) -3,897 -,075(xy)
H -3,897 4,429(xx) -,907(xy)
FH ,075(yx) ,907(yx) ,051(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) H DSQ
1 1 2,896 1,000 ,00 ,00 ,00
2 9,722E-02 5,458 ,11 ,00 ,24
3 6,495E-03 21,117 ,88 1,00 ,76
a Dependent Variable: FH

EQUATION 18

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fH H Dsq/ ORIGIN/ STATISTICS = all/ DEPENDENT = fH/
METHOD = ENTER H Dsq.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,02

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b,c)
Model Variables Entered Variables Removed Method
1 DSQ, H(a) , Enter
a All requested variables entered.
b Dependent Variable: FH
c Linear Regression through the Origin





Model Summary

R R Square(a) Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,999(b) ,998 ,998 ,293264 ,998 73199,083 2 348 ,000 -856,684 ,002 2,000 -848,968
a For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models which include an intercept.
b Predictors: DSQ, H

ANOVA(c,d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 12590,755 2 6295,378 73199,083 ,000(a)
Residual 29,929 348 8,600E-02

Total 12620,684(b) 350


a Predictors: DSQ, H
b This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.
c Dependent Variable: FH
d Linear Regression through the Origin



Coefficients(a,b)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 H ,433 ,004 ,986 ,010 102,274 ,000 ,425 ,442 ,999 ,984 ,267 ,073 13,631
DSQ 7,027 4,972 ,014 ,010 1,413 ,158 -2,753 16,806 ,962 ,076 ,004 ,073 13,631
a Dependent Variable: FH
b Linear Regression through the Origin

Coefficient Correlations(a,b)
Model DSQ H
1 Correlations DSQ 1,000 -,963
H -,963 1,000
Covariances DSQ 24,724 -2,028E-02
H -2,028E-02 1,795E-05
a Dependent Variable: FH
b Linear Regression through the Origin

Swept Correlation Matrix(a,b)

Columns
Model Rows DSQ H FH
1 DSQ 13,631(xx) -13,121 -,014(xy)
H -13,121 13,631(xx) -,986(xy)
FH ,014(yx) ,986(yx) ,002(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FH
b Linear Regression through the Origin



Collinearity Diagnostics(a,b)

Eigenvalue Condition Index Variance Proportions
Model Dimension H DSQ
1 1 1,963 1,000 ,02 ,02
2 3,738E-02 7,246 ,98 ,98
a Dependent Variable: FH
b Linear Regression through the Origin

EQUATION 19

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fHl Dl Dl2/ STATISTICS = all/
DEPENDENT = fHl/ METHOD = ENTER Dl Dl2.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 DL2, DL(a) , Enter
a All requested variables entered.
b Dependent Variable: FHL





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,963(a) ,927 ,927 5,986E-02 ,927 2217,545 2 347 ,000 -1968,021 ,074 3,000 -1956,447
a Predictors: (Constant), DL2, DL

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 15,893 2 7,946 2217,545 ,000(a)
Residual 1,243 347 3,583E-03

Total 17,136 349


a Predictors: (Constant), DL2, DL
b Dependent Variable: FHL



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) 1,306 ,257

5,088 ,000 ,801 1,810




DL -1,490 ,225 -1,351 ,204 -6,618 ,000 -1,932 -1,047 ,949 -,335 -,096 ,005 199,314
DL2 -,556 ,049 -2,306 ,204 -11,295 ,000 -,653 -,459 -,958 -,518 -,163 ,005 199,314
a Dependent Variable: FHL

Coefficient Correlations(a)
Model DL2 DL
1 Correlations DL2 1,000 ,997
DL ,997 1,000
Covariances DL2 2,425E-03 1,106E-02
DL 1,106E-02 5,067E-02
a Dependent Variable: FHL

Swept Correlation Matrix(a)

Columns
Model Rows DL2 DL FHL
1 DL2 199,314(xx) 198,813 2,306(xy)
DL 198,813 199,314(xx) 1,351(xy)
FHL -2,306(yx) -1,351(yx) ,073(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FHL



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) DL DL2
1 1 2,986 1,000 ,00 ,00 ,00
2 1,401E-02 14,601 ,01 ,00 ,00
3 2,477E-05 347,203 ,99 1,00 1,00
a Dependent Variable: FHL

EQUATION 20

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fHl Dl Hl/ STATISTICS = all/ DEPENDENT = fHl/
METHOD = ENTER Dl Hl.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b)
Model Variables Entered Variables Removed Method
1 HL, DL(a) , Enter
a All requested variables entered.
b Dependent Variable: FHL





Model Summary

R R Square Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 ,979(a) ,958 ,958 4,560E-02 ,958 3946,571 2 347 ,000 -2158,470 ,043 3,000 -2146,896
a Predictors: (Constant), HL, DL

ANOVA(b)
Model Sum of Squares df Mean Square F Sig.
1 Regression 16,414 2 8,207 3946,571 ,000(a)
Residual ,722 347 2,080E-03

Total 17,136 349


a Predictors: (Constant), HL, DL
b Dependent Variable: FHL



Coefficients(a)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 (Constant) -,109 ,199

-,545 ,586 -,501 ,284




DL ,148 ,043 ,135 ,039 3,442 ,001 ,064 ,233 ,949 ,182 ,038 ,079 12,611
HL ,856 ,039 ,849 ,039 21,697 ,000 ,778 ,934 ,978 ,759 ,239 ,079 12,611
a Dependent Variable: FHL

Coefficient Correlations(a)
Model HL DL
1 Correlations HL 1,000 -,960
DL -,960 1,000
Covariances HL 1,557E-03 -1,633E-03
DL -1,633E-03 1,861E-03
a Dependent Variable: FHL

Swept Correlation Matrix(a)

Columns
Model Rows HL DL FHL
1 HL 12,611(xx) -12,100 -,849(xy)
DL -12,100 12,611(xx) -,135(xy)
FHL ,849(yx) ,135(yx) ,042(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FHL



Collinearity Diagnostics(a)

Eigenvalue Condition Index Variance Proportions
Model Dimension (Constant) DL HL
1 1 2,986 1,000 ,00 ,00 ,00
2 1,437E-02 14,413 ,00 ,02 ,02
3 9,940E-05 173,304 1,00 ,98 ,98
a Dependent Variable: FHL

EQUATION 21

Regression

Notes
Output Created 19-OCT-2004 09:31:35
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\FormHeight-Diameter-Height\fh_d_h.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 350
Missing Value Handling Definition of Missing User-defined missing values are treated as missing.
Cases Used Statistics are based on cases with no missing values for any variable used.
Syntax REGRESSION VARIABLES = fHl Dl Hl/ ORIGIN/ STATISTICS = all/ DEPENDENT = fHl/
METHOD = ENTER Dl Hl.
Resources Memory Required 1764 bytes
Additional Memory Required for Residual Plots 0 bytes
Elapsed Time 0:00:00,01

Warnings
STATISTICS keywords LINE, END, and HISTORY are no longer supported.

Variables Entered/Removed(b,c)
Model Variables Entered Variables Removed Method
1 HL, DL(a) , Enter
a All requested variables entered.
b Dependent Variable: FHL
c Linear Regression through the Origin





Model Summary

R R Square(a) Adjusted R Square Std. Error of the Estimate Change Statistics Selection Criteria
Model R Square Change F Change df1 df2 Sig. F Change Akaike Information Criterion Amemiya Prediction Criterion Mallows' Prediction Criterion Schwarz Bayesian Criterion
1 1,000(b) ,999 ,999 4,556E-02 ,999 260840,510 2 348 ,000 -2160,171 ,001 2,000 -2152,455
a For regression through the origin (the no-intercept model), R Square measures the proportion of the variability in the dependent variable about the origin explained by regression. This CANNOT be compared to R Square for models which include an intercept.
b Predictors: HL, DL

ANOVA(c,d)
Model Sum of Squares df Mean Square F Sig.
1 Regression 1082,683 2 541,342 260840,510 ,000(a)
Residual ,722 348 2,075E-03

Total 1083,405(b) 350


a Predictors: HL, DL
b This total sum of squares is not corrected for the constant because the constant is zero for regression through the origin.
c Dependent Variable: FHL
d Linear Regression through the Origin



Coefficients(a,b)

Unstandardized Coefficients Standardized Coefficients t Sig. 95% Confidence Interval for B Correlations Collinearity Statistics
Model B Std. Error Beta Std. Error Lower Bound Upper Bound Zero-order Partial Part Tolerance VIF
1 DL ,172 ,006 ,227 ,008 27,745 ,000 ,160 ,184 -,978 ,830 ,038 ,029 35,042
HL ,835 ,006 1,223 ,008 149,269 ,000 ,824 ,846 ,999 ,992 ,207 ,029 35,042
a Dependent Variable: FHL
b Linear Regression through the Origin

Coefficient Correlations(a,b)
Model HL DL
1 Correlations HL 1,000 ,986
DL ,986 1,000
Covariances HL 3,127E-05 3,412E-05
DL 3,412E-05 3,831E-05
a Dependent Variable: FHL
b Linear Regression through the Origin

Swept Correlation Matrix(a,b)

Columns
Model Rows HL DL FHL
1 HL 35,042(xx) 34,539 -1,223(xy)
DL 34,539 35,042(xx) -,227(xy)
FHL 1,223(yx) ,227(yx) ,001(yy)
xx This variable is an independent variable.
xy Row variable is an independent variable, column variable is the dependent variable.
yx Row variable is the independent variable, column variable is an independent variable.
yy This variable is the dependent variable.
a Dependent Variable: FHL
b Linear Regression through the Origin



Collinearity Diagnostics(a,b)

Eigenvalue Condition Index Variance Proportions
Model Dimension DL HL
1 1 1,986 1,000 ,01 ,01
2 1,437E-02 11,754 ,99 ,99
a Dependent Variable: FHL
b Linear Regression through the Origin