Springer Texts in Business and Economics
Multiple Regression Analysis
4.1 The regressions for parts (a), (b), (c), (d) and (e) are given below.
a. Regression of LNC on LNP and LNY Dependent Variable: LNC
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Analysis of Variance
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B. H. Baltagi, Solutions Manual for Econometrics, Springer Texts in Business and Economics, DOI 10.1007/978-3-642-54548-1—4, © Springer-Verlag Berlin Heidelberg 2015
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Parameter |
Standard |
T for HO: |
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Variable |
DF |
Estimate |
Error |
Parameter=0 |
Prob>|T| |
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INTERCEP |
1 |
5.094108 |
0.06269897 |
81.247 |
0.0001 |
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LNP |
1 |
-1.198316 |
0.28178857 |
-4.253 |
0.0001 |
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c. Regression of LNY on |
LNP |
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Dependent Variable: LNY |
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Analysis of Variance |
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Sum of |
Mean |
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Source |
DF |
Squares |
Square |
F Value |
Prob > F |
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Model |
1 |
0.22075 |
0.22075 |
14.077 |
0.0005 |
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Error |
44 |
0.68997 |
0.01568 |
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C Total |
45 |
0.91072 |
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Root MSE |
0.12522 |
R-square |
0.2424 |
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Dep Mean |
4.77546 |
Adj R-sq |
0.2252 |
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C. V. |
2.62225 |
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Parameter Estimates |
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Parameter |
Standard |
T for HO: |
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Variable |
DF |
Estimate |
Error |
Parameter=0 |
Prob>|T| |
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INTERCEP |
1 |
4.608533 |
0.04816809 |
95.676 |
0.0001 |
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LNP |
1 |
0.812239 |
0.21648230 |
3.752 |
0.0005 |
d. Regression of LNC on the residuals of part (c). Dependent Variable: LNC
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Analysis of Variance
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RootMSE 0.19241 R-square 0.0124
DepMean 4.84784 Adj R-sq -0.0100
C. V. 3.96907
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Variable |
DF |
Parameter Estimate |
Standard Error |
T for HO: Parameter=0 |
Prob>|T| |
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INTERCEP |
1 |
4.847844 |
0.02836996 |
170.879 |
0.0001 |
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RESID. C |
1 |
0.172386 |
0.23164467 |
0.744 |
0.4607 |
e. Regression of Residuals from part (b) on those from part (c).
Dependent Variable: RESID. B
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Analysis of Variance
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f. The multiple regression coefficient estimate of real income in part (a) is equal to the slope coefficient of the regressions in parts (d) and (e). This demonstrates the residualing out interpretation of multiple regression coefficients.
