THU 3/11/99 12:31:52 PM SYSTAT VERSION 7.0.1 COPYRIGHT (C) 1997, SPSS INC. Welcome to SYSTAT! >USE 'C:\SYSTAT7\DATA\LONGLEY.SYD' SYSTAT Rectangular file C:\SYSTAT7\DATA\LONGLEY.SYD, created Tue Feb 18, 1986 at 13:56:00, contains variables: DEFLATOR GNP UNEMPLOY ARMFORCE POPULATN TIME TOTAL
The Longley data set is provided as part of the SYSTAT package. It is a highly
collinear data set used to test the accuracy of regression programs. The dependent
variable TOTAL is total employment.
>mglh >model total = constant + deflator + gnp + unemploy + armforce + populatn + time >estimate Dep Var: TOTAL N: 16 Multiple R: 0.997737 Squared multiple R: 0.995479 Adjusted squared multiple R: 0.992465 Standard error of estimate: 304.854074 Effect Coefficient Std Error Std Coef Tolerance t P(2 Tail) CONSTANT -3.48226E+06 8.90420E+05 0.0 . -3.91080 0.00356 DEFLATOR 15.061872 84.914926 0.046282 0.007378 0.17738 0.86314 GNP -0.035819 0.033491 -1.013746 0.000559 -1.06952 0.31268 UNEMPLOY -2.020230 0.488400 -0.537543 0.029745 -4.13643 0.00254 ARMFORCE -1.033227 0.214274 -0.204741 0.278635 -4.82199 0.00094 POPULATN -0.051104 0.226073 -0.101221 0.002505 -0.22605 0.82621 TIME 1829.151465 455.478499 2.479664 0.001318 4.01589 0.00304 Analysis of Variance Source Sum-of-Squares df Mean-Square F-ratio P Regression 1.84172E+08 6 3.06954E+07 330.285339 0.000000 Residual 8.36424E+05 9 9.29360E+04 ------------------------------------------------------------------------------- Durbin-Watson D Statistic 2.559 First Order Autocorrelation -0.348
Example 1 - Coefficient simultaneously (jointly) = 0
>hypothesis >specify deflator=0; gnp=0; populatn=0 >test
Hypothesis. A Matrix 1 2 3 4 5 1 0.0 -1.000000 0.0 0.0 0.0 2 0.0 0.0 -1.000000 0.0 0.0 3 0.0 0.0 0.0 0.0 0.0 6 7 1 0.0 0.0 2 0.0 0.0 3 -1.000000 0.0 D Matrix 1 0.0 2 0.0 3 0.0 Test of Hypothesis Source SS df MS F P Hypothesis 4.86937E+05 3 1.62312E+05 1.746495 0.227032 Error 8.36424E+05 9 9.29360E+04
Example 2 - Difference of 2 coefficients = 0 >hypothesis >specify gnp-populatn=0 >test
Hypothesis. A Matrix 1 2 3 4 5 0.0 0.0 -1.000000 0.0 0.0 6 7 1.000000 0.0 Null hypothesis value for D 0.0 Test of Hypothesis Source SS df MS F P Hypothesis 334.822931 1 334.822931 0.003603 0.953449 Error 8.36424E+05 9 9.29360E+04
Example 3 - Coefficient of one variable 3 times coefficient of another >hypothesis >specify unemploy=3*armforce >test
Hypothesis. A Matrix 1 2 3 4 5 0.0 0.0 0.0 -1.000000 3.000000 6 7 0.0 0.0 Null hypothesis value for D 0.0 Test of Hypothesis Source SS df MS F P Hypothesis 4.11199E+05 1 4.11199E+05 4.424544 0.064754 Error 8.36424E+05 9 9.29360E+04
Example 4 - Coefficients of 2 variables have specific nonzero values >hypothesis >specify populatn=0.5; time=1000 >test
Hypothesis. A Matrix 1 2 3 4 5 1 0.0 0.0 0.0 0.0 0.0 2 0.0 0.0 0.0 0.0 0.0 6 7 1 -1.000000 0.0 2 0.0 -1.000000 D Matrix 1 -0.500000 2 -1000.000000 Test of Hypothesis Source SS df MS F P Hypothesis 1.38981E+06 2 6.94907E+05 7.477265 0.012214 Error 8.36424E+05 9 9.29360E+04
Example 5 - Difference between 2 coefficients has a specific nonzero value >hypothesis >specify deflator-unemploy=20 >test
Hypothesis. A Matrix 1 2 3 4 5 0.0 -1.000000 0.0 1.000000 0.0 6 7 0.0 0.0 Null hypothesis value for D -20.000000 Test of Hypothesis Source SS df MS F P Hypothesis 109.038029 1 109.038029 0.001173 0.973423 Error 8.36424E+05 9 9.29360E+04
Example 6 - Same as 5, but specifying a less plausible (more extreme) difference >hypothesis >specify deflator-unemploy=500 >test
Hypothesis. A Matrix 1 2 3 4 5 0.0 -1.000000 0.0 1.000000 0.0 6 7 0.0 0.0 Null hypothesis value for D -500.000000 Test of Hypothesis Source SS df MS F P Hypothesis 2.98665E+06 1 2.98665E+06 32.136635 0.000306 Error 8.36424E+05 9 9.29360E+04 Note that this time the test is "significant": one would conclude H1 and reject the null hypothesis
Last modified 11 March 1999