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Chapter 12: 140SE (page 807)

It is desired to relate E(y) to a quantitative variable x1 and a qualitative variable at three levels.

  1. Write a first-order model.
  2. Write a model that will graph as three different second- order curves—one for each level of the qualitative variable.

Short Answer

Expert verified
  1. A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written as E(y)=β0+β1xx+β2xx+β3x3.
  2. Graph

Step by step solution

01

First-order model

A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written asE(y)=β0+β1xx+β2xx+β3x3,

Where x1 is the quantitative variable

And x2 and x­3 represent level 1 and level 2 of the qualitative variable.

02

Graph

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Most popular questions from this chapter

Suppose you fit the regression model Ey=β0+β1x1+β2x2+β3x22+β4x1x2+β5x1x222 to n = 35 data points and wish to test the null hypothesis H0:β4=β5=0

  1. State the alternative hypothesis.

  2. Explain in detail how to compute the F-statistic needed to test the null hypothesis.

  3. What are the numerator and denominator degrees of freedom associated with the F-statistic in part b?

  4. Give the rejection region for the test if α = .05.

Write a model relating E(y) to one qualitative independent variable that is at four levels. Define all the terms in your model.

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)=β0+β1x1+β2x22+β3x2+β4x1x2+β5x12x2

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: 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.

Consider the following data that fit the quadratic modelE(y)=β0+β1x+β2x2:

a. Construct a scatterplot for this data. Give the prediction equation and calculate R2based on the model above.

b. Interpret the value ofR2.

c. Justify whether the overall model is significant at the 1% significance level if the data result into a p-value of 0.000514.
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