Question #62

The appropriate number of dummy variables is one less than the number of categories because the intercept captures the effect of the other effect. With 12 categories (months) the appropriate number of dummy variables is 11 = 12 – 1. If the number of dummy variables equals the number of categories, it is possible to state any one of the independent dummy variables in terms of the others. This is a violation of the assumption of the multiple linear regression model that none of the independent variables are linearly related. (Module 1.4, LOS 1.l) Damon Washburn, CFA, is currently enrolled as a part-time graduate student at State University. One of his recent assignments for his course on Quantitative Analysis is to perform a regression analysis utilizing the concepts covered during the semester. He must interpret the results of the regression as well as the test statistics. Washburn is confident in his ability to calculate the statistics because the class is allowed to use statistical software. However, he realizes that the interpretation of the statistics will be the true test of his knowledge of regression analysis. His professor has given to the students a list of questions that must be answered by the results of the analysis. Washburn has estimated a regression equation in which 160 quarterly returns on the S&P 500 are explained by three macroeconomic variables: employment growth (EMP) as measured by nonfarm payrolls, gross domestic product (GDP) growth, and private investment (INV). The results of the regression analysis are as follows: Coefficient Estimates Parameter Coefficient Standard Error of Coefficient Intercept 9.50 3.40 EMP -4.50 1.25 GDP 4.20 0.76 INV -0.30 0.16 Other Data: Regression sum of squares (RSS) = 126.00 Sum of squared errors (SSE) = 267.00 BG-stat: Lag 1: 3.15; Lag 2: 3.22 Degree of Freedom Denominator Degree of Freedom Numerator 1 2 3 153 3.90 3.06 2.66 154 3.90 3.05 2.66 155 3.90 3.05 2.66 156 3.90 3.05 2.66 157 3.90 3.05 2.66 158 3.90 3.05 2.66