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Chapter 12: Q141SE (page 807)

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

Short Answer

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Step-wise regression is used to streamline the number of variables used in the model. To build a model with large number of independent variables is very difficult because of the interpretation of multivariable terms and interactions in the model. Therefore, step-wise regression analysis is used to streamline and select the number of variable which explain the data in the best way.

Step by step solution

01

Step wise regression

Step-wise regression is used to streamline the number of variables used in the model.

02

Value in model-building process

To build a model with large number of independent variables is very difficult because of the interpretation of multivariable terms and interactions in the model. Therefore, step-wise regression analysis is used to streamline and select the number of variable which explain the data in the best way.

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Most popular questions from this chapter

Production technologies, terroir, and quality of Bordeaux wine. In addition to state-of-the-art technologies, the production of quality wine is strongly influenced by the natural endowments of the grape-growing region鈥攃alled the 鈥渢erroir.鈥� The Economic Journal (May 2008) published an empirical study of the factors that yield a quality Bordeaux wine. A quantitative measure of wine quality (y) was modeled as a function of several qualitative independent variables, including grape-picking method (manual or automated), soil type (clay, gravel, or sand), and slope orientation (east, south, west, southeast, or southwest).

  1. Create the appropriate dummy variables for each of the qualitative independent variables.
  2. Write a model for wine quality (y) as a function of grape-picking method. Interpret the尾鈥檚 in the model.
  3. Write a model for wine quality (y) as a function of soil type. Interpret the尾鈥檚 in the model.
  4. Write a model for wine quality (y) as a function of slope orientation. Interpret the尾鈥檚 in the model.

Question: Consider the model:

y=尾0+尾1x1+尾2x2+尾3x3+蔚

where x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels using the coding scheme

role="math" localid="1649846492724" x2=1鈥�鈥�鈥�iflevel鈥�20鈥�鈥�otherwise鈥�鈥�鈥�鈥�鈥�鈥�鈥�x3=1鈥�鈥�鈥�if鈥�level鈥�30鈥�鈥�鈥�otherwise

The resulting least squares prediction equation is y^=44.8+2.2x1+9.4x2+15.6x3

a. What is the response line (equation) for E(y) when x2 = x3 = 0? When x2 = 1 and x3 = 0? When x2 = 0 and x3 = 1?

b. What is the least squares prediction equation associated with level 1? Level 2? Level 3? Plot these on the same graph.

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 a college student鈥檚 decision to undergo cosmetic surgery, Exercise 12.17 (p. 725). Recall that the data for the study (simulated based on statistics reported in the journal article) are saved in the file. Consider the interaction model, , where y = desire to have cosmetic surgery (25-point scale), = {1 if male, 0 if female}, and = impression of reality TV (7-point scale). The model was fit to the data and the resulting SPSS printout appears below.

a.Give the least squares prediction equation.

b.Find the predicted level of desire (y) for a male college student with an impression-of-reality-TV-scale score of 5.

c.Conduct a test of overall model adequacy. Use a= 0.10.

d.Give a practical interpretation of R2a.

e.Give a practical interpretation of s.

f.Conduct a test (at a = 0.10) to determine if gender (x1) and impression of reality TV show (x4) interact in the prediction of level of desire for cosmetic surgery (y).

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.

Going for it on fourth down in the NFL. Refer to the Chance (Winter 2009) study of fourth-down decisions by coaches in the National Football League (NFL), Exercise 11.69 (p. 679). Recall that statisticians at California State University, Northridge, fit a straight-line model for predicting the number of points scored (y) by a team that has a first-down with a given number of yards (x) from the opposing goal line. A second model fit to data collected on five NFL teams from a recent season was the quadratic regression model, E(y)=尾0+尾1x+尾2x2.The regression yielded the following results: y=6.13+0.141x-0.0009x2,R2=0.226.

a) If possible, give a practical interpretation of each of the b estimates in the model.

b) Give a practical interpretation of the coefficient of determination,R2.

c) In Exercise 11.63, the coefficient of correlation for the straight-line model was reported asR2=0.18. Does this statistic alone indicate that the quadratic model is a better fit than the straight-line model? Explain.

d) What test of hypothesis would you conduct to determine if the quadratic model is a better fit than the straight-line model?
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