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Chapter 12: 141SE (page 807)

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

Short Answer

Expert verified

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

Consider the model:

E(y)=β0+β1x1+β2x2+β3x22+β4x3+β5x1x22

where x2 is a quantitative model and

x1=(1receivedtreatment0didnotreceivetreatment)

The resulting least squares prediction equation is

localid="1649802968695" y⏜=2+x1-5x2+3x22-4x3+x1x22

a. Substitute the values for the dummy variables to determine the curves relating to the mean value E(y) in general form.

b. On the same graph, plot the curves obtained in part a for the independent variable between 0 and 3. Use the least squares prediction equation.

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’s 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).

Question: Consider the model:

y=β0+β1x1+β2x2+β3x3+ε

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   iflevel 20  otherwise       x3=1   if level 30   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.

Consider fitting the multiple regression model

Ey=β0+β1x1+β2x2+β3x3+β4x4+β5x5

A matrix of correlations for all pairs of independent variables is given below. Do you detect a multicollinearity problem? Explain.
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