Question

2. A multiple linear regression model of the following form is fitted to a data set Yi = ?? + ??xi? + ??xi? + ?i, ?i ~ N(0, ?²)i.i.d. The model is fitted using SAS and the following output is obtained: Sum of mean Source DF Squares Square F Value Pr > F Model 2 28.119 14.059 ? 0.0039 Error 3 0.715 ? Corrected Total 5 28.833 Parameter Standard Variable Estimate Error t Value Pr > |t| Intercept 2.105 0.422 4.99 0.0155 x? 1.242 0.119 10.42 0.0019 x? -0.195 0.439 ? ? (a) Find the sample size. (b) Find mean squared errors (MSE). (c) Find R². (d) Find the value for the F-test statistic. (e) What hypotheses the above F test for? Given ? = 0.05, what conclusion will you have? (f) One wants to test H? : ?? = 0 vs H? : ?? ? 0. Find the value of test statistic and make your conclusion at ? = .05.

          2. A multiple linear regression model of the following form is fitted to a data set
Yi = ?? + ??xi? + ??xi? + ?i, ?i ~ N(0, ?²)i.i.d.
The model is fitted using SAS and the following output is obtained:
Sum of mean
Source DF Squares Square F Value Pr > F
Model 2 28.119 14.059 ? 0.0039
Error 3 0.715 ?
Corrected Total 5 28.833
Parameter Standard
Variable Estimate Error t Value Pr > |t|
Intercept 2.105 0.422 4.99 0.0155
x? 1.242 0.119 10.42 0.0019
x? -0.195 0.439 ? ?
(a) Find the sample size.
(b) Find mean squared errors (MSE).
(c) Find R².
(d) Find the value for the F-test statistic.
(e) What hypotheses the above F test for? Given ? = 0.05, what conclusion will you have?
(f) One wants to test H? : ?? = 0 vs H? : ?? ? 0. Find the value of test statistic and make your conclusion at ? = .05.

2. A multiple linear regression model of the following form is fitted to a data set
Yi = ?? + ??xi? + ??xi? + ?i, ?i N(0, ?²)i.i.d.
The model is fitted using SAS and the following output is obtained:
Sum of mean
Source DF Squares Square F Value Pr > F
Model 2 28.119 14.059 ? 0.0039
Error 3 0.715 ?
Corrected Total 5 28.833
Parameter Standard
Variable Estimate Error t Value Pr > |t|
Intercept 2.105 0.422 4.99 0.0155
x? 1.242 0.119 10.42 0.0019
x? -0.195 0.439 ? ?
(a) Find the sample size.
(b) Find mean squared errors (MSE).
(c) Find R².
(d) Find the value for the F-test statistic.
(e) What hypotheses the above F test for? Given ? = 0.05, what conclusion will you have?
(f) One wants to test H? : ?? = 0 vs H? : ?? ? 0. Find the value of test statistic and make your conclusion at ? = .05.

Added by Lori O.

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