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Chapter 12: 142SE (page 708)

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).

Short Answer

Expert verified
  1. A first-order model for E(y) with two quantitative variables x1and x2 can be written asEy=β0+β1x1+β2x2+ε.
  2. A Second-order model for E(y) with two quantitative variables x1and x2 can be written asEy=β0+β1x1+β2x2+β3x12+β4x22+ε .

Step by step solution

01

First-order model for E(y)

A first-order model for E(y) with two quantitative variables x1and x2 can be written as Ey=β0+β1x1+β2x2+ε.

02

Second-order model for E(y)

A Second-order model for E(y) with two quantitative variables x1and x2 can be written as Ey=β0+β1x1+β2x2+β3x12+β4x22+ε.

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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)=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: The complete modelE(y)=β0+β1x1+β2x2+β3x3+β4x4+εwas fit to n = 20 data points, with SSE = 152.66. The reduced model,E(y)=β0+β1x1+β2x2+ε, was also fit, with

SSE = 160.44.

a. How many β parameters are in the complete model? The reduced model?

b. Specify the null and alternative hypotheses you would use to investigate whether the complete model contributes more information for the prediction of y than the reduced model.

c. Conduct the hypothesis test of part b. Use α = .05.

To model the relationship between y, a dependent variable, and x, an independent variable, a researcher has taken one measurement on y at each of three different x-values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order model Ey=β0+β1x+β2x2 and it will pass exactly through all three points, yielding SSE = 0. The researcher, delighted with the excellent fit of the model, eagerly sets out to use it to make inferences. What problems will he encounter in attempting to make inferences?

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