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Chapter 12: 125E (page 803)

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 = .983.
  2. The correlation relating number of females in managerial positions and number of female high school graduates with no college degree: r = .074.
  3. The correlation relating number of males in managerial positions and number of males with a college degree: r = .722.
  4. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r = .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

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: Write a regression model relating E(y) to a qualitative independent variable that can assume three levels. Interpret all the terms in the model.

Consider relating E(y) to two quantitative independent variables x1 and x2.

  1. Write a first-order model for E(y).

  2. Write a complete second-order model for E(y).

Question: Estimating repair and replacement costs of water pipes. Refer to the IHS Journal of Hydraulic Engineering (September, 2012) study of the repair and replacement of water pipes, Exercise 11.21 (p. 655). Recall that a team of civil engineers used regression analysis to model y = the ratio of repair to replacement cost of commercial pipe as a function of x = the diameter (in millimeters) of the pipe. Data for a sample of 13 different pipe sizes are reproduced in the accompanying table. In Exercise 11.21, you fit a straight-line model to the data. Now consider the quadratic model,E(y)=β0+β1x+β2x2. A Minitab printout of the analysis follows (next column).

  1. Give the least squares prediction equation relating ratio of repair to replacement cost (y) to pipe diameter (x).
  2. Conduct a global F-test for the model usingα=0.01. What do you conclude about overall model adequacy?
  3. Evaluate the adjusted coefficient of determination,Ra2, for the model.
  4. Give the null and alternative hypotheses for testing if the rate of increase of ratio (y) with diameter (x) is slower for larger pipe sizes.
  5. Carry out the test, part d, using α=0.01.
  6. Locate, on the printout, a 95% prediction interval for the ratio of repair to replacement cost for a pipe with a diameter of 240 millimeters. Interpret the result.

Question: Bus Rapid Transit study. Bus Rapid Transit (BRT) is a rapidly growing trend in the provision of public transportation in America. The Center for Urban Transportation Research (CUTR) at the University of South Florida conducted a survey of BRT customers in Miami (Transportation Research Board Annual Meeting, January 2003). Data on the following variables (all measured on a 5-point scale, where 1 = very unsatisfied and 5 = very satisfied) were collected for a sample of over 500 bus riders: overall satisfaction with BRT (y), safety on bus (x1), seat availability (x2), dependability (x3), travel time (x4), cost (x5), information/maps (x6), convenience of routes (x7), traffic signals (x8), safety at bus stops (x9), hours of service (x10), and frequency of service (x11). CUTR analysts used stepwise regression to model overall satisfaction (y).

a. How many models are fit at step 1 of the stepwise regression?

b. How many models are fit at step 2 of the stepwise regression?

c. How many models are fit at step 11 of the stepwise regression?

d. The stepwise regression selected the following eight variables to include in the model (in order of selection): x11, x4, x2, x7, x10, x1, x9, and x3. Write the equation for E(y) that results from stepwise regression.

e. The model, part d, resulted in R2 = 0.677. Interpret this value.

f. Explain why the CUTR analysts should be cautious in concluding that the best model for E(y) has been found.
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