Fox Module 10: Advanced multiple regression HW


Fox Module 10: Advanced multiple regression HW

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NEAS
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Module 10: Advanced multiple regression

(The attached PDF file has better formatting.)

Homework assignment: Two correlated independent variables

Do this homework assignment after module 12, which gives the equations for the standard errors of the least squares estimators.

We regress the Y values on the X1 and X2 values in the table below.

X1

X2

Y

X1

X2

Y

1

1

1.016

6

8

-1.076

2

6

-3.429

7

4

3.461

3

2

0.049

8

9

-2.525

4

7

-3.099

9

5

4.195

5

3

0.359

10

10

-0.746

What is the correlation of X1 and X2?

What is the least squares estimator of

á?

What is the least squares estimator of

â1, the coefficient of X1?

What is the least squares estimator of

â2, the coefficient of X2?

What is the standard error of the least squares estimator of

â1, the coefficient of X1?

What is the standard error of the least squares estimator of

â2, the coefficient of X2?

Show the formulas and the computations. You can check your work with Excel or other statistical software.


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NEAS
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Jacob: When using the equation on page 106 and page 107, what is R2? Is R2 the value from the Excel regression add-in using these two explanatory variables?



Rachel:

No, the R2 in the equation on page 106 and page 107 is the correlation of the two explanatory variables, or the R2 from a regression on one on the other. If one have more than two explanatory variables, it is the R2 from a regression of the explanatory variable under consideration on all the other explanatory variables.



Illustration:

In this homework assignment, the R2 from the regression on the response variable on the two explanatory variables is 0.8712. The correlation of the two explanatory variables is 0.6364. Use 0.6364 in the equation, not 0.8712.

In this homework assignment, the R2 from the regression on the response variable on the two explanatory variables is 0.8712. The correlation of the two explanatory variables is 0.6364. Use 0.6364 in the equation, not 0.8712.


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