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Chapter 12: Q119E (page 782)

Question: After-death album sales. When a popular music artist dies, sales of the artist鈥檚 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 鈥渂est鈥� model for predicting y? Explain. If not, outline a strategy for finding the best model.

Short Answer

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Answer

Stepwise regression model is used when there are a lot of independent variables to consider for explaining the dependent variable. In this case, there are only 2 independent variables: album publicity and artist death status. Using stepwise regression would be time consuming and inefficient.

The significance of the model can be tested using an F-test and individual t-test for individual 尾 parameters.

Step by step solution

01

Stepwise regression

Stepwise regression model is used when there are a lot of independent variables to consider for explaining the dependent variable. In this case, there are only 2 independent variables: album publicity and artist death status. Using stepwise regression would be time consuming and inefficient.

02

 Step 2: Best model for the data

The significance of the model can be tested using an F-test and individual t-test for individual 尾 parameters.

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Most popular questions from this chapter

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

Question: Suppose you fit the interaction model y=尾0+尾1x1+尾2x2+尾3x1x2+蔚 to n = 32 data points and obtain the following results:SSyy=479,鈥�SSE=21,鈥�尾^3=10, and s尾^3=4

a. Find R2and interpret its value.

b. Is the model adequate for predicting y? Test at 伪=.05

c. Use a graph to explain the contribution of the x1 , x2 term to the model.

d. Is there evidence that x1and x2 interact? Test at 伪=.05 .

Suppose you have developed a regression model to explain the relationship between y and x1, x2, and x3. The ranges of the variables you observed were as follows: 10 鈮� y 鈮� 100, 5 鈮� x1 鈮� 55, 0.5 鈮� x2 鈮� 1, and 1,000 鈮� x3 鈮� 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x1 = 30, x2 = 0.6, and x3 = 1,300, or when x1 = 60, x2 = 0.4, and x3 = 900? Why?

Question: There are six independent variables, x1, x2, x3, x4, x5, and x6, that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The software fits all possible one-variable models of the form

E(Y)=尾0+尾1xi

where xi is the ith independent variable, i = 1, 2, 鈥�, 6. The information in the table is provided from the computer printout.

a. Which independent variable is declared the best one variable predictor of y? Explain.

b. Would this variable be included in the model at this stage? Explain.

c. Describe the next phase that a stepwise procedure would execute.

Question: Suppose you fit the first-order multiple regression model y=尾0+尾1x1+尾2x2+蔚 to n=25 data points and obtain the prediction equationy^=6.4+3.1x1+0.92x2 . The estimated standard deviations of the sampling distributions of 尾1 and 尾2are 2.3 and .27, respectively
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