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Chapter 12: Q125E (page 803)

Question: Women in top management. Refer to the Journal of Organizational Culture, Communications and Conflict (July 2007) study on women in upper management positions at U.S. firms, Exercise 11.73 (p. 679). Monthly data (n = 252 months) were collected for several variables in an attempt to model the number of females in managerial positions (y). The independent variables included the number of females with a college degree (x1), the number of female high school graduates with no college degree (x2), the number of males in managerial positions (x3), the number of males with a college degree (x4), and the number of male high school graduates with no college degree (x5). The correlations provided in Exercise 11.67 are given in each part. Determine which of the correlations results in a potential multicollinearity problem for the regression analysis.

  1. The correlation relating number of females in managerial positions and number of females with a college degree: r =0.983.

  2. The correlation relating number of females in managerial positions and number of female high school graduates with no college degree: r =0.074.

  3. The correlation relating number of males in managerial positions and number of males with a college degree: r =0.722.

  4. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r =0.528.

Short Answer

Expert verified

  1. There is high level of multicollinearity between y and x1

  2. There is low level of multicollinearity between y and x2.

  3. There is moderate level of multicollinearity between x3 and x4.

  4. There is moderate level of multicollinearity between x3 and x5.

Step by step solution

01

Multicollinearity check

The r value between number of females in managerial positions (y) and number of females with a college degree (x1) is 0.983 which is very high degree of correlation.

Hence there is high level of multicollinearity between y and x1.

02

Multicollinearity check

The r value between number of females in managerial positions (y) and number of female high school graduates with no college degree (x2) is 0.074 which is very low degree of correlation.

Hence there is low level of multicollinearity between y and x2.

03

Multicollinearity check

The r value between number of males in managerial positions (x3) and number of males with a college degree (x4) is 0.722 which is moderate degree of correlation.

Hence there is moderate level of multicollinearity between x3 and x4.

04

Multicollinearity check

The r value between number of males in managerial positions (x3) and number of male high school graduates with no college degree (x5) is 0.528 which is moderate degree of correlation.

Hence there is moderate level of multicollinearity between x3 and x5.

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Most popular questions from this chapter

Question: Glass as a waste encapsulant. Because glass is not subject to radiation damage, encapsulation of waste in glass is considered to be one of the most promising solutions to the problem of low-level nuclear waste in the environment. However, chemical reactions may weaken the glass. This concern led to a study undertaken jointly by the Department of Materials Science and Engineering at the University of Florida and the U.S. Department of Energy to assess the utility of glass as a waste encapsulant. Corrosive chemical solutions (called corrosion baths) were prepared and applied directly to glass samples containing one of three types of waste (TDS-3A, FE, and AL); the chemical reactions were observed over time. A few of the key variables measured were

y = Amount of silicon (in parts per million) found in solution at end of experiment. (This is both a measure of the degree of breakdown in the glass and a proxy for the amount of radioactive species released into the environment.)

x1 = Temperature (°C) of the corrosion bath

x2 = 1 if waste type TDS-3A, 0 if not

x3 = 1 if waste type FE, 0 if not

(Waste type AL is the base level.) Suppose we want to model amount y of silicon as a function of temperature (x1) and type of waste (x2, x3).

a. Write a model that proposes parallel straight-line relationships between amount of silicon and temperature, one line for each of the three waste types.

b. Add terms for the interaction between temperature and waste type to the model of part a.

c. Refer to the model of part b. For each waste type, give the slope of the line relating amount of silicon to temperature.

e. Explain how you could test for the presence of temperature–waste type interaction.

Question: Risk management performance. An article in the International Journal of Production Economics (Vol. 171, 2016) investigated the factors associated with a firm’s supply chain risk management performance (y). Five potential independent variables (all measured quantitatively) were considered: (1) firm size, (2) supplier orientation, (3) supplier dependency, (4) customer orientation, and (5) systemic purchasing. Consider running a stepwise regression to find the best subset of predictors for risk management performance.

a. How many 1-variable models are fit in step 1 of the stepwise regression?

b. Assume supplier orientation is selected in step 1. How many 2-variable models are fit in step 2 of the stepwise regression?

c. Assume systemic purchasing is selected in step 2. How many 3-variable models are fit in step 3 of the stepwise regression?

d. Assume customer orientation is selected in step 3. How many 4-variable models are fit in step 4 of the stepwise regression?

e. Through the first 4 steps of the stepwise regression, determine the total number of t-tests performed. Assuming each test uses an a = .05 level of significance, give an estimate of the probability of at least one Type I error in the stepwise regression.

Consider the model:

E(y)=β0+β1x1+β2x2+β3x22+β4x3+β5x1x22

where x2 is a quantitative model and

x1=(1receivedtreatment0didnotreceivetreatment)

The resulting least squares prediction equation is

localid="1649802968695" y⏜=2+x1-5x2+3x22-4x3+x1x22

a. Substitute the values for the dummy variables to determine the curves relating to the mean value E(y) in general form.

b. On the same graph, plot the curves obtained in part a for the independent variable between 0 and 3. Use the least squares prediction equation.

Buy-side vs. sell-side analysts’ earnings forecasts. Refer to the Financial Analysts Journal (July/August 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86 (p. 112). The Harvard Business School professors used regression to model the relative optimism (y) of the analysts’ 3-month horizon forecasts. One of the independent variables used to model forecast optimism was the dummy variable x = {1 if the analyst worked for a buy-side firm, 0 if the analyst worked for a sell-side firm}.

a) Write the equation of the model for E(y) as a function of type of firm.

b) Interpret the value ofβ0in the model, part a.

c) The professors write that the value ofβ1in the model, part a, “represents the mean difference in relative forecast optimism between buy-side and sell-side analysts.” Do you agree?

d) The professors also argue that “if buy-side analysts make less optimistic forecasts than their sell-side counterparts, the [estimated value ofβ1] will be negative.” Do you agree?

Question: The Excel printout below resulted from fitting the following model to n = 15 data points: y=β0+β1x1+β2x2+ε

Where,

x1=(1iflevel20ifnot)x2=(1iflevel30ifnot)

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