Reading 12: Multiple Regression and Issues in Regression A

class, white, black, overall

Q50. Hays decides to test the overall effectiveness of the both independent variables in explaining sales for Milky Way. Assuming that the total sum of squares is 389.14, the sum of squared errors is 146.85 and the mean squared error is 2.576, calculate and interpret the R².

A) The R² equals 0.242, indicating that the two independent variables account for 24.2% of the variation in monthly sales.

B) The R² equals 0.623, indicating that the two independent variables account for 37.7% of the variation in monthly sales.

C) The R² equals 0.623, indicating that the two independent variables account for 62.3% of the variation in monthly sales.

Q51. Stepp is concerned about the validity of Hays’ regression analysis and asks Hays if he can test for the presence of heteroskedasticity. Hays complies with Stepp’s request, and detects the presence of unconditional heteroskedasticity. Which of the following statements regarding heteroskedasticity is most correct?

A) Heteroskedasticity can be detected either by examining scatter plots of the residual or by using the Durbin-Watson test.

B) Unconditional heteroskedasticity usually causes no major problems with the regression.

C) Unconditional heteroskedasticity does create significant problems for statistical inference.

Q52. John Rains, CFA, is a professor of finance at a large university located in the Eastern United States. He is actively involved with his local chapter of the Society of Financial Analysts. Recently, he was asked to teach one session of a Society-sponsored CFA review course, specifically teaching the class addressing the topic of quantitative analysis. Based upon his familiarity with the CFA exam, he decides that the first part of the session should be a review of the basic elements of quantitative analysis, such as hypothesis testing, regression and multiple regression analysis. He would like to devote the second half of the review session to the practical application of the topics he covered in the first half.

Rains decides to construct a sample regression analysis case study for his students in order to demonstrate a “real-life” application of the concepts. He begins by compiling financial information on a fictitious company called Big Rig, Inc. According to the case study, Big Rig is the primary producer of the equipment used in the exploration for and drilling of new oil and gas wells in the United States. Rains has based the information in the problem on an actual equity holding in his personal portfolio, but has simplified the data for the purposes of the review course.

Rains constructs a basic regression model for Big Rig in order to estimate its profitability (in millions), using two independent variables: the number of new wells drilled in the U.S. (WLS) and the number of new competitors (COMP) entering the market:

Profits = b₀ + b₁WLS – b₂COMP + ε

Based on the model, the estimated regression equation is:

Profits = 22.5 + 0.98(WLS) − 0.35(COMP)

Using the past 5 years of quarterly data, he calculated the following regression estimates for Big Rig, Inc:

Coefficient

Standard Error

Intercept

22.5

2.465

WLS

0.98

0.683