AGEC 317



AGEC 317

Homework #3

Spring 2004

The following paired observations, are used in this homework. You must show all your work to obtain credit for this homework. You must show your calculations. Stating I did it on a calculator will not suffice for this homework.

|Y-Values |X - Values |

|40 |4 |

|60 |3 |

|80 |5 |

1. Calculate the OLS estimates for a and b in the following equation,[pic], using the matrix form of the OLS estimator.

a) Are the estimates the same as in homework #2? Why or why not?

b) What is the proper interpretation of [pic]?

c) What is the proper interpretation of [pic]?

2. The matrix formula for calculating the variance of the intercept and slope parameters is [pic]where [pic]. Variances of the intercept and slope are given by the diagonal elements of the matrix. The first diagonal element is the variance associated with [pic] and the second diagonal element is the variance associated with [pic]. For more detail, see the inference reading assignment. The off-diagonal elements of the matrix give the covariance between the estimated parameters. Future lectures will provide more information on the use of this formula. Calculate the standard error of the estimates for a and b.

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