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Chapter 12: Q138SE (page 807)

The first-order model E(y)=尾0+尾1x1was fit to n = 19 data points. A residual plot for the model is provided below. Is the need for a quadratic term in the model evident from the residual plot? Explain.


Short Answer

Expert verified

The residual plot indicates a strong positive relation among dependent and independent variable. And since the residual points are clustered around in a straight line, the graph is indicating a linear relationship among y and x. Since the graph indicates a linear relationship between dependent and independent variable, there is no need for an additional quadratic term in the model.

Step by step solution

01

Residual plot

The residual plot indicates a strong positive relation among dependent and independent variable. And since the residual points are clustered around in a straight line, the graph is indicating a linear relationship among y and x.

02

Need for quadratic term

Since the graph indicates a linear relationship between dependent and independent variable, there is no need for an additional quadratic term in the model.

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Most popular questions from this chapter

Explain why stepwise regression is used. What is its value in the model-building process?

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=尾0+尾1x+尾2x2 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?

Question: Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on one鈥檚 desire to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that psychologists used multiple regression to model desire to have cosmetic surgery (y) as a function of gender(x1) , self-esteem(x2) , body satisfaction(x3) , and impression of reality TV (x4). The SPSS printout below shows a confidence interval for E(y) for each of the first five students in the study.

  1. Interpret the confidence interval for E(y) for student 1.
  2. Interpret the confidence interval for E(y) for student 4

Question: Risk management performance. An article in the International Journal of Production Economics (Vol. 171, 2016) investigated the factors associated with a firm鈥檚 supply chain risk management performance (y). Five potential independent variables (all measured quantitatively) were considered: (1) firm size, (2) supplier orientation, (3) supplier dependency, (4) customer orientation, and (5) systemic purchasing. Consider running a stepwise regression to find the best subset of predictors for risk management performance.

a. How many 1-variable models are fit in step 1 of the stepwise regression?

b. Assume supplier orientation is selected in step 1. How many 2-variable models are fit in step 2 of the stepwise regression?

c. Assume systemic purchasing is selected in step 2. How many 3-variable models are fit in step 3 of the stepwise regression?

d. Assume customer orientation is selected in step 3. How many 4-variable models are fit in step 4 of the stepwise regression?

e. Through the first 4 steps of the stepwise regression, determine the total number of t-tests performed. Assuming each test uses an a = .05 level of significance, give an estimate of the probability of at least one Type I error in the stepwise regression.

Suppose the mean value E(y) of a response y is related to the quantitative independent variables x1and x2

E(y)=2+x1-3x2-x1x2

a) Identify and interpret the slope forx2

b) Plot the linear relationship between E(y) andx2for role="math" localid="1649796003444" x1=0,1,2, whererole="math" localid="1649796025582" 1鈮�x2鈮�3

c) How would you interpret the estimated slopes?

d) Use the lines you plotted in part b to determine the changes in E(y) for eachrole="math" localid="1649796051071" x1=0,1,2.

e) Use your graph from part b to determine how much E(y) changes whenrole="math" localid="1649796075921" 3鈮�x1鈮�5androle="math" localid="1649796084395" 1鈮�x2鈮�3.
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