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Chapter 12: Q119E (page 782)

Question: After-death album sales. When a popular music artist dies, sales of the artist’s albums often increase dramatically. A study of the effect of after-death publicity on album sales was published in Marketing Letters (March 2016). The following data were collected weekly for each of 446 albums of artists who died a natural death: album publicity (measured as the total number of printed articles in which the album was mentioned at least once during the week), artist death status (before or after death), and album sales (dollars). Suppose you want to use the data to model weekly album sales (y) as a function of album publicity and artist death status. Do you recommend using stepwise regression to find the “best” model for predicting y? Explain. If not, outline a strategy for finding the best model.

Short Answer

Expert verified

Answer

Stepwise regression model is used when there are a lot of independent variables to consider for explaining the dependent variable. In this case, there are only 2 independent variables: album publicity and artist death status. Using stepwise regression would be time consuming and inefficient.

The significance of the model can be tested using an F-test and individual t-test for individual β parameters.

Step by step solution

01

Stepwise regression

Stepwise regression model is used when there are a lot of independent variables to consider for explaining the dependent variable. In this case, there are only 2 independent variables: album publicity and artist death status. Using stepwise regression would be time consuming and inefficient.

02

 Step 2: Best model for the data

The significance of the model can be tested using an F-test and individual t-test for individual β parameters.

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Most popular questions from this chapter

Question: Determine which pairs of the following models are “nested” models. For each pair of nested models, identify the complete and reduced model.

a.E(y)=β0+β1x1+β2x2b.E(y)=β0+β1x1c.E(y)=β0+β1x1+β2x12d.E(y)=β0+β1x1+β2x2+β3x1x2e.E(y)=β0+β1x1+β2x2+β3x1x2+β4x21+β5x22

Question: Failure times of silicon wafer microchips. Refer to the National Semiconductor study of manufactured silicon wafer integrated circuit chips, Exercise 12.63 (p. 749). Recall that the failure times of the microchips (in hours) was determined at different solder temperatures (degrees Celsius). The data are repeated in the table below.

  1. Fit the straight-line modelEy=β0+β1xto the data, where y = failure time and x = solder temperature.

  2. Compute the residual for a microchip manufactured at a temperature of 149°C.

  3. Plot the residuals against solder temperature (x). Do you detect a trend?

  4. In Exercise 12.63c, you determined that failure time (y) and solder temperature (x) were curvilinearly related. Does the residual plot, part c, support this conclusion?

Service workers and customer relations. A study in Industrial Marketing Management (February 2016) investigated the impact of service workers’ (e.g., waiters and waitresses) personal resources on the quality of the firm’s relationship with customers. The study focused on four types of personal resources: flexibility in dealing with customers(x1), service worker reputation(x2), empathy for the customer(x3), and service worker’s task alignment(x4). A multiple regression model was employed used to relate these four independent variables to relationship quality (y). Data were collected for n = 220 customers who had recent dealings with a service worker. (All variables were measured on a quantitative scale, based on responses to a questionnaire.)

a) Write a first-order model for E(y) as a function of the four independent variables. Refer to part

Which β coefficient measures the effect of flexibility(x1)on relationship quality (y), independently of the other

b) independent variables in the model?

c) Repeat part b for reputation(x2), empathy(x3), and task alignment(x4).

d) The researchers theorize that task alignment(x4)“moderates” the effect of each of the other x’s on relationship quality (y) — that is, the impact of eachx, x1,x2, orx3on y depends on(x4). Write an interaction model for E(y) that matches the researchers’ theory.

e) Refer to part d. What null hypothesis would you test to determine if the effect of flexibility(x1)on relationship quality (y) depends on task alignment(x4)?

f) Repeat part e for the effect of reputation(x2)and the effect of empathy(x3).

g) None of the t-tests for interaction were found to be “statistically significant”. Given these results, the researchers concluded that their theory was not supported. Do you agree?

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.

Suppose you fit the model y =β0+β1x1+β1x22+β3x2+β4x1x2+εto n = 25 data points with the following results:

β^0=1.26,β^1= -2.43,β^2=0.05,β^3=0.62,β^4=1.81sβ^1=1.21,sβ^2=0.16,sβ^3=0.26, sβ^4=1.49SSE=0.41 and R2=0.83

  1. Is there sufficient evidence to conclude that at least one of the parameters b1, b2, b3, or b4 is nonzero? Test using a = .05.

  2. Test H0: β1 = 0 against Ha: β1 < 0. Use α = .05.

  3. Test H0: β2 = 0 against Ha: β2 > 0. Use α = .05.

  4. Test H0: β3 = 0 against Ha: β3 ≠ 0. Use α = .05.
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