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Unformatted text preview: ECON 1150 Fall 2010 Problem Set 3: Due 10/25/10 Please be sure that the pages are stapled together in the correct order. Please write neatly. Parts within each question receive equal weight. You do not need to attach Stata output with your answers, but be sure to write out all equations in standard form; and include the sample size and the R-squared. 1. Provide a short answer to each of the following questions. (i) Suppose that the results of a multiple and simple regression, using the same set of data, are and Are x 1 and x 2 positively or negatively correlated in the sample? Justify your answer. (Hint: use formula (3.23) on page 84) Using equation connecting coefficients estimates of the simple and multiple regression, one can obtain , a slope coefficient form a simple regression of x 2 on x 1 : The negative sign of the slope coefficient indicates negative correlation between x 2 and x 1. (ii) Comment on the following statement: Multiple regression analysis is useless unless all of the explanatory variables are uncorrelated. As long as there is no perfect collinearity between the independent variables, regression makes sense, since inclusion of each independent variable allows a researcher to hold it fixed in the analysis. It is true that if the explanatory variables are highly correlated that it may be difficult to estimate each partial effect, but that depends on other factors, such as the sample size and how big the population effect is. In any case, correlations among the explanatory variables are certainly allowed, and fully expected, in multiple regression. (iii) Let math4 be the pass rate, in percent, on a 4 th grade math test, and let str denote the student-teacher ratio. For 745 schools, the following simple regression is estimated: , 2 Now suppose I redefine the pass rate to be the fraction of students passing; call the new...
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This note was uploaded on 02/20/2011 for the course ECON 1150 taught by Professor Staff during the Fall '08 term at Pittsburgh.
- Fall '08