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Chapter 12: Q111E (page 781)

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.

Short Answer

Expert verified

Answer

a. For x1, the t-value is the highest (3.80), x1 is the best one variable predictor of y.

b. Since x1 is the best one-variable predictor of y, the variable will be included in the model at this stage.

c. The stepwise program now begins to search through the remaining (k 鈥� 1) independent variables for the best two-variable model of the form. Therefore, here the program begins searching remaining 5 independent variables for the best two-variable model.

Step by step solution

01

One-variable best predictor

T-test values for testing of single 尾 parameter is尾i^s尾i^

Here for x1, x2,x3,x4,x5,and x6t-values are 3.80, -90, 2.98, 1.21, -6.02, and 0.857 respectively. Since for x1, the t-value is the highest, x1 is the best one variable predictor of y.

02

Stepwise procedure

Since x1 is the best one-variable predictor of y, the variable will be included in the model at this stage.

03

Stepwise procedure

The stepwise program now begins to search through the remaining (k 鈥� 1) independent variables for the best two-variable model of the form. Therefore, here the program begins searching remaining 5 independent variables for the best two-variable model

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Most popular questions from this chapter

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.

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?

Ascorbic acid reduces goat stress. Refer to the Animal Science Journal (May, 2014) study on the use of ascorbic acid (AA) to reduce stress in goats during transportation from farm to market, Exercise 9.12 (p. 529). Recall that 24 healthy goats were randomly divided into four groups (A, B, C, and D) of six animals each. Goats in group A were administered a dosage of AA 30 minutes prior to transportation; goats in group B were administered a dosage of AA 30 minutes following transportation; group C goats were not given any AA prior to or following transportation; and, goats in group D were not given any AA and were not transported. Weight was measured before and after transportation and the weight loss (in kilograms) determined for each goat.

  1. Write a model for mean weight loss, E(y), as a function of the AA dosage group (A, B, C, or D). Use group D as the base level.
  2. Interpret the鈥檚 in the model, part a.
  3. Recall that the researchers discovered that mean weight loss is reduced in goats administered AA compared to goats not given any AA. On the basis of this result, determine the sign (positive or negative) of as many of the鈥檚 in the model, part a, as possible.

Question: Refer to Exercise 12.82.

a. Write a complete second-order model that relates E(y) to the quantitative variable.

b. Add the main effect terms for the qualitative variable (at three levels) to the model of part a.

c. Add terms to the model of part b to allow for interaction between the quantitative and qualitative independent variables.

d. Under what circumstances will the response curves of the model have the same shape but different y-intercepts?

e. Under what circumstances will the response curves of the model be parallel lines?

f. Under what circumstances will the response curves of the model be identical?

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