Results: l09.sas

The REG Procedure

Model: MODEL1

Dependent Variable: lv

The Reg Procedure

MODEL1

Fit

lv

Number of Observations

Number of Observations Read 31
Number of Observations Used 31

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares
Mean
Square
F Value Pr > F
Model 4 8.12928 2.03232 294.53 <.0001
Error 26 0.17941 0.00690    
Corrected Total 30 8.30869      

Fit Statistics

Root MSE 0.08307 R-Square 0.9784
Dependent Mean 3.27273 Adj R-Sq 0.9751
Coeff Var 2.53818    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate
Standard
Error
t Value Pr > |t|
Intercept 1 -1.94349 1.95775 -0.99 0.3300
Girth 1 0.27389 0.04563 6.00 <.0001
g2 1 -0.00454 0.00161 -2.83 0.0089
Height 1 0.04894 0.05544 0.88 0.3855
h2 1 -0.00022203 0.00036986 -0.60 0.5535

The REG Procedure

Model: MODEL1

Dependent Variable: lv

Observation-wise Statistics

lv

Diagnostic Plots

Fit Diagnostics

Panel of fit diagnostics for lv.

Residual Plots

Panel 1

Panel of scatterplots of residuals by regressors for lv.

The Transreg Procedure

Log(Volume)


The TRANSREG Procedure

Dependent Variable Log(Volume)

Number of Observations

Number of Observations Read 31
Number of Observations Used 31

The TRANSREG Procedure Hypothesis Tests for Log(Volume)

ANOVA

Univariate ANOVA Table Based on the Usual Degrees of Freedom
Source DF Sum of Squares Mean Square F Value Pr > F
Model 2 8.123226 4.061613 613.19 <.0001
Error 28 0.185463 0.006624    
Corrected Total 30 8.308690      
Root MSE 0.08139 R-Square 0.9777
Dependent Mean 3.27273 Adj R-Sq 0.9761
Coeff Var 2.48679    

Coefficients

Univariate Regression Table Based on the Usual Degrees of Freedom
Variable DF Coefficient Type II
Sum of
Squares
Mean Square F Value Pr > F
Intercept 1 -6.6316171 0.45539 0.45539 68.75 <.0001
Log(Girth) 1 1.9826499 4.62750 4.62750 698.63 <.0001
Log(Height) 1 1.1171233 0.19778 0.19778 29.86 <.0001

The Transreg Procedure

Log(Volume)


The TRANSREG Procedure

Dependent Variable Log(Volume)

Number of Observations

Number of Observations Read 31
Number of Observations Used 31

The TRANSREG Procedure Hypothesis Tests for Log(Volume)

ANOVA

Univariate ANOVA Table Based on the Usual Degrees of Freedom
Source DF Sum of Squares Mean Square F Value Pr > F
Model 4 8.129282 2.032321 294.53 <.0001
Error 26 0.179407 0.006900    
Corrected Total 30 8.308690      
Root MSE 0.08307 R-Square 0.9784
Dependent Mean 3.27273 Adj R-Sq 0.9751
Coeff Var 2.53818    

Coefficients

Univariate Regression Table Based on the Usual Degrees of Freedom
Variable DF Coefficient Type II
Sum of
Squares
Mean Square F Value Pr > F
Intercept 1 -1.9434909 0.00680 0.00680 0.99 0.3300
Identity(Girth) 1 0.2738856 0.24860 0.24860 36.03 <.0001
Identity(Height) 1 0.0489426 0.00538 0.00538 0.78 0.3855
Power(Girth) 1 -0.0045434 0.05523 0.05523 8.00 0.0089
Power(Height) 1 -0.0002220 0.00249 0.00249 0.36 0.5535

Spline Data for Arsenic

The TRANSREG Procedure

The Transreg Procedure

Identity(nails)

Iteration History

TRANSREG MORALS Algorithm Iteration History for Identity(nails)
Iteration
Number
Average
Change
Maximum
Change
R-Square Criterion
Change
Note
1 0.17015 1.42089 0.80356    
2 0.00000 0.00000 0.92174 0.11817 Converged
Algorithm converged.

Fit Plot

Spline Regression Fit for nails and water

Loess Smoothing for Arsenic

The LOESS Procedure

The Loess Procedure

Scaling Information

Independent Variable Scaling
Scaling applied: None
Statistic water
Minimum Value 0
Maximum Value 0.13700

Loess Smoothing for Arsenic

The LOESS Procedure

Dependent Variable: nails

 

Optimal Smoothing Criterion

Optimal Smoothing Criterion
AICC Smoothing
Parameter
-1.55025 1.00000

Loess Smoothing for Arsenic

The LOESS Procedure

Selected Smoothing Parameter: 1

Dependent Variable: nails

Selected Model

Fit Summary

Fit Summary
Fit Method kd Tree
Blending Linear
Number of Observations 21
Number of Fitting Points 7
kd Tree Bucket Size 4
Degree of Local Polynomials 2
Smoothing Parameter 1.00000
Points in Local Neighborhood 21
Residual Sum of Squares 0.96584
Trace[L] 3.18368
GCV 0.00304
AICC -1.55025
AICC1 -32.60741
Delta1 17.88968
Delta2 17.88588
Equivalent Number of Parameters 3.25705
Lookup Degrees of Freedom 17.89348
Residual Standard Error 0.23235

Fit Plot

Fit plot of nails by water with 95% confidence limits for smoothing parameter 1.