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.