Question

1. A multiple linear regression model of the following form is fitted to a data set Yi = ?0 + ?1xi1 + ?2xi2 + ?3xi3 + ?i, ?i ~ N(0, ?2)i.i.d. The model is fitted using SAS and the following output is obtained: Source DF Sum of Squares mean Square F Value Pr > F Model 3 2667.79 889.26 ? < 0.0001 Error 9 47.97 ? Corrected Total 12 2715.76 Variable Parameter Estimate Standard Error t Value Pr > |t| Intercept 71.648 14.142 5.07 0.0007 x1 1.452 0.117 12.41 < .0001 x2 0.416 0.186 2.24 0.0517 x3 -0.237 0.173 ? 0.2054 (a) Find the sample size. (b) Find MSE. (c) Find R2 and explain it’s meaning. (d) Find adjusted R2. (e) Find the value for the F-test statistic. (f) What hypotheses the F-test? Please set up the null hypothesis and alternative hypothesis. (g) Given ? = 0.05, what conclusion will you have for the above test? (h) One wish to test H0 : ?3 = 0 vs Ha : ?3 ? 0. Please calculate the test statistic.

          1. A multiple linear regression model of the following form is fitted to a data set
Yi = ?0 + ?1xi1 + ?2xi2 + ?3xi3 + ?i, ?i ~ N(0, ?2)i.i.d.
The model is fitted using SAS and the following output is obtained:
Source DF Sum of Squares mean Square F Value Pr > F
Model 3 2667.79 889.26 ? < 0.0001
Error 9 47.97 ?
Corrected Total 12 2715.76
Variable Parameter Estimate Standard Error t Value Pr > |t|
Intercept 71.648 14.142 5.07 0.0007
x1 1.452 0.117 12.41 < .0001
x2 0.416 0.186 2.24 0.0517
x3 -0.237 0.173 ? 0.2054
(a) Find the sample size.
(b) Find MSE.
(c) Find R2 and explain it’s meaning.
(d) Find adjusted R2.
(e) Find the value for the F-test statistic.
(f) What hypotheses the F-test? Please set up the null hypothesis and alternative hypothesis.
(g) Given ? = 0.05, what conclusion will you have for the above test?
(h) One wish to test H0 : ?3 = 0 vs Ha : ?3 ? 0. Please calculate the test statistic.

1. A multiple linear regression model of the following form is fitted to a data set
Yi = ?0 + ?1xi1 + ?2xi2 + ?3xi3 + ?i, ?i N(0, ?2)i.i.d.
The model is fitted using SAS and the following output is obtained:
Source DF Sum of Squares mean Square F Value Pr > F
Model 3 2667.79 889.26 ? < 0.0001
Error 9 47.97 ?
Corrected Total 12 2715.76
Variable Parameter Estimate Standard Error t Value Pr > |t|
Intercept 71.648 14.142 5.07 0.0007
x1 1.452 0.117 12.41 < .0001
x2 0.416 0.186 2.24 0.0517
x3 -0.237 0.173 ? 0.2054
(a) Find the sample size.
(b) Find MSE.
(c) Find R2 and explain it’s meaning.
(d) Find adjusted R2.
(e) Find the value for the F-test statistic.
(f) What hypotheses the F-test? Please set up the null hypothesis and alternative hypothesis.
(g) Given ? = 0.05, what conclusion will you have for the above test?
(h) One wish to test H0 : ?3 = 0 vs Ha : ?3 ? 0. Please calculate the test statistic.

Added by Morgan C.

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