Reading 12: Multiple Regression and Issues in Regression Analysis

LOS a, (Part 1): Formulate a multiple regression equation to describe the relation between a dependent variable and several independent variables, and determine the statistical significance of each independent variable

1.Milky Way, Inc. is a large manufacturer of children’s toys and games based in the United States. Their products have high name brand recognition, and have been sold in retail outlets throughout the United States for nearly fifty years. The founding management team was bought out by a group of investors five years ago. The new management team, led by Russell Stepp, decided that Milky Way should try to expand its sales into the Western European market, which had never been tapped by the former owners. Under Stepp’s leadership, additional personnel are hired in the Research and Development department, and a new marketing plan specific to the European market is implemented. Being a new player in the European market, Stepp knows that it will take several years for Milky Way to establish its brand name in the marketplace, and is willing to make the expenditures now in exchange for increased future profitability.

Now, five years after entering the European market, Stepp is reviewing the results of his plan. Sales in Europe have slowly but steadily increased over since Milky Way’s entrance into the market, but profitability seems to have leveled out. Stepp decides to hire a consultant, Ann Hays, CFA, to review and evaluate their European strategy. One of Hays’ first tasks on the job is to perform a regression analysis on Milky Way’s European sales. She is seeking to determine whether the additional expenditures on research and development and marketing for the European market should be continued in the future.

Hays begins by establishing a relationship between the European sales of Milky Way (in millions of dollars) and the two independent variables, the number of dollars (in millions) spent on research and development (R&D) and marketing (MKTG). Based upon five years of monthly data, Hays constructs the following estimated regression equation:

Estimated Sales = 54.82 + 5.97 (MKTG) + 1.45 (R&D)

Additionally, Hays calculates the following regression estimates:

Hays begins the analysis by determining if both of the independent variables are statistically significant. To test whether a coefficient is statistically significant means to test whether it is statistically significantly different from:

A)   the upper tail critical value.

B)   slope coefficient.

C)   zero.

D)   the lower tail critical value.

The correct answer was C)

The magnitude of the coefficient reveals nothing about the importance of the independent variable in explaining the dependent variable. Therefore, it must be determined if each independent variable is statistically significant. The null hypothesis is that the slope coefficient for each independent variable equals zero.