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Solutions_to_Homework_3 - PAM 305 Introduction to...

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PAM 305 - Introduction to Multivariate Analysis Fall 2006 Suggested Solutions Homework 3 Due date: September 29th Question 1 For the computer exercises in STATA we will use the same data set WAGE1.dta. Suppose that the true model is log( wage ) = β o + β 1 educ + β 2 exper + β 3 tenure + u (1) Obtain the sample regression function d log( wage ) = ˆ β o + ˆ β 1 educ + ˆ β 2 exper + ˆ β 3 tenure (2) a. As in the simple linear regression model, the coefficients have a percent- age interpretation. The only difference is that now they have a ceteris paribus interpretation. Interpret ˆ β 1 . ˆ β 1 =0.092 is the ceteris paribus effect of education on wages, that is the effect of education on wage, holding fixed tenure and experience. An extra year of education will, on average, increase wages by ˆ β 1 × 100 percent, i.e. 9.2% b. If we take two people with the same levels of experience and job tenure, what is the percentage difference in predicted wages if their education differs by 1 year? The percentage difference in predicted wages will be 9.2%. Remember that the beauty of multiple regression analysis is to allow us to explicitly 1
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control for many factors that simultaneously affect the dependent vari- able. We can study the effect of one explanatory variable on the explained variable holding the others fixed, even though those other factors were not being held fixed during the sampling process.
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