Results: product.sas

Test H0: beta1 * beta2 = 0 on the SAT data

Proc reg to get starting values

The REG Procedure

Model: MODEL1

Dependent Variable: gpa

The Reg Procedure

MODEL1

Fit

gpa

Number of Observations

Number of Observations Read 200
Number of Observations Used 200

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 2 7.77445 3.88723 12.93 <.0001
Error 197 59.23635 0.30069    
Corrected Total 199 67.01080      

Fit Statistics

Root MSE 0.54835 R-Square 0.1160
Dependent Mean 2.63010 Adj R-Sq 0.1070
Coeff Var 20.84917    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 0.60807 0.44131 1.38 0.1698
verbal 1 0.00231 0.00055213 4.18 <.0001
math 1 0.00099736 0.00060947 1.64 0.1033

Test H0: beta1 * beta2 = 0 on the SAT data

Testing H0: beta1 beta2 = 0

The NLMIXED Procedure

The Nlmixed Procedure

Specifications

Specifications
Data Set WORK.PENNSTATE
Dependent Variable gpa
Distribution for Dependent Variable Normal
Optimization Technique Dual Quasi-Newton
Integration Method None

Dimensions

Dimensions
Observations Used 200
Observations Not Used 0
Total Observations 200
Parameters 4

Initial Parameters

Initial Parameters
beta0 beta1 beta2 sigmasq Negative
Log
Likelihood
0.60807 0.00231 0.000997 0.30069 162.121924

Iteration History

Iteration History
Iteration Calls Negative
Log
Likelihood		 Difference Maximum
Gradient		 Slope
1 10 162.1209 0.001066 4.98620 -11096.6
2 15 162.1208 0.00002 5.30041 -0.52211
3 18 162.1095 0.011336 7.23140 -0.47384
4 20 162.1095 3.192E-6 0.11012 -6.54E-6
5 22 162.1095 2.012E-9 0.001313 -4.03E-9

Convergence Status

NOTE: GCONV convergence criterion satisfied.

Fit Statistics

Fit Statistics
-2 Log Likelihood 324.2
AIC (smaller is better) 332.2
AICC (smaller is better) 332.4
BIC (smaller is better) 345.4

Parameter Estimates

Parameter Estimates
Parameter Estimate Standard
Error		 DF t Value Pr > |t| 95% Confidence Limits Gradient
beta0 0.6081 0.4382 200 1.39 0.1667 -0.2559 1.4721 -0.00002
beta1 0.002307 0.000548 200 4.21 <.0001 0.001226 0.003388 0.001313
beta2 0.000997 0.000605 200 1.65 0.1008 -0.00020 0.002190 0.000743
sigmasq 0.2962 0.02963 200 10.00 <.0001 0.2378 0.3546 0.000010

Contrasts

Contrasts
Label Num DF Den DF F Value Pr > F
Product 1 200 2.90 0.0903