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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: Job performance under time pressure. Refer to the Academy of Management Journal (October 2015) study of how time pressure affects team job performance, Exercise 12.89 (p. 765). Recall that the researchers hypothesized a complete second-order model relating team performance (y) to perceived time pressure (x1), and whether or not the team had an effective leader (x2 = 1 if yes, 0 if no):

E(Y)=尾0+尾1x1+尾2x22+尾3x2+尾4x1x2+尾5x12x2

a) How would you determine whether the rate of increase of team performance with time pressure depends on effectiveness of the team leader?

b) For fixed time pressure, how would you determine whether the mean team performance differs for teams with effective and non-effective team leaders?

Question: Accuracy of software effort estimates. Periodically, software engineers must provide estimates of their effort in developing new software. In the Journal of Empirical Software Engineering (Vol. 9, 2004), multiple regression was used to predict the accuracy of these effort estimates. The dependent variable, defined as the relative error in estimating effort, y = (Actual effort - Estimated effort)/ (Actual effort) was determined for each in a sample of n = 49 software development tasks. Eight independent variables were evaluated as potential predictors of relative error using stepwise regression. Each of these was formulated as a dummy variable, as shown in the table.

Company role of estimator: x1 = 1 if developer, 0 if project leader

Task complexity: x2 = 1 if low, 0 if medium/high

Contract type: x3 = 1 if fixed price, 0 if hourly rate

Customer importance: x4 = 1 if high, 0 if low/medium

Customer priority: x5 = 1 if time of delivery, 0 if cost or quality

Level of knowledge: x6 = 1 if high, 0 if low/medium

Participation: x7 = 1 if estimator participates in work, 0 if not

Previous accuracy: x8 = 1 if more than 20% accurate, 0 if less than 20% accurate

a. In step 1 of the stepwise regression, how many different one-variable models are fit to the data?

b. In step 1, the variable x1 is selected as the best one- variable predictor. How is this determined?

c. In step 2 of the stepwise regression, how many different two-variable models (where x1 is one of the variables) are fit to the data?

d. The only two variables selected for entry into the stepwise regression model were x1 and x8. The stepwise regression yielded the following prediction equation:

Give a practical interpretation of the 尾 estimates multiplied by x1 and x8.

e) Why should a researcher be wary of using the model, part d, as the final model for predicting effort (y)?

Question: Novelty of a vacation destination. Many tourists choose a vacation destination based on the newness or uniqueness (i.e., the novelty) of the itinerary. The relationship between novelty and vacationing golfers鈥� demographics was investigated in the Annals of Tourism Research (Vol. 29, 2002). Data were obtained from a mail survey of 393 golf vacationers to a large coastal resort in the south-eastern United States. Several measures of novelty level (on a numerical scale) were obtained for each vacationer, including 鈥渃hange from routine,鈥� 鈥渢hrill,鈥� 鈥渂oredom-alleviation,鈥� and 鈥渟urprise.鈥� The researcher employed four independent variables in a regression model to predict each of the novelty measures. The independent variables were x1 = number of rounds of golf per year, x2 = total number of golf vacations taken, x3 = number of years played golf, and x4 = average golf score.

  1. Give the hypothesized equation of a first-order model for y = change from routine.
  1. A test of H0: 尾3 = 0 versus Ha: 尾3< 0 yielded a p-value of .005. Interpret this result if 伪 = .01.
  1. The estimate of 尾3 was found to be negative. Based on this result (and the result of part b), the researcher concluded that 鈥渢hose who have played golf for more years are less apt to seek change from their normal routine in their golf vacations.鈥� Do you agree with this statement? Explain.
  1. The regression results for three dependent novelty measures, based on data collected for n = 393 golf vacationers, are summarized in the table below. Give the null hypothesis for testing the overall adequacy of the first-order regression model.
  1. Give the rejection region for the test, part d, for 伪 = .01.
  1. Use the test statistics reported in the table and the rejection region from part e to conduct the test for each of the dependent measures of novelty.
  1. Verify that the p-values reported in the table support your conclusions in part f.
  1. Interpret the values of R2 reported in the table.

Question: Failure times of silicon wafer microchips. Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer-Level Packaging Conference, November 3鈥�4, 2005). The failure times of the microchips (in hours) were determined at different solder temperatures (degrees Celsius). The data for one experiment are given in the table. The researchers want to predict failure time (y) based on solder temperature (x).

  1. Construct a scatterplot for the data. What type of relationship, linear or curvilinear, appears to exist between failure time and solder temperature?
  2. Fit the model,E(y)=尾0+尾1x+尾2x2, to the data. Give the least-squares prediction equation.
  3. Conduct a test to determine if there is upward curvature in the relationship between failure time and solder temperature. (use.伪=0.05)

Question:Consider the first-order model equation in three quantitative independent variables E(Y)=2-3x1+5x2-x3

  1. Graph the relationship between Y and x3for x1=2 and x2=1
  2. Repeat part a for x1=1and x2=-2
  3. How do the graphed lines in parts a and b relate to each other? What is the slope of each line?
  4. If a linear model is first-order in three independent variables, what type of geometric relationship will you obtain when is graphed as a function of one of the independent variables for various combinations of the other independent variables?
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