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Chapter 12: Q121E (page 802)

Consider fitting the multiple regression model

E(y)= 尾0+尾1x1+ 尾2x2+尾3x3+ 尾4x4 +尾5x5

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


Short Answer

Expert verified

In this question, x4 and x2 has a correlation of 0.93 and x4 and x5 has a correlation of 0.86. These correlation numbers are very high indicating a strong positive relationship between x4 and x2 and x4 and x5 respectively. Thus, the problem of multicollinearity exists in the model.

Step by step solution

01

Multicollinearity check

Multicollinearity is checked by checking the correlation amongst the independent variables. If there is high correlation amongst any two independent variables, it is said that the problem of multicollinearity exists in the model.

02

Application of multicollinearity check

In this question, x4 and x2 has a correlation of 0.93 and x4 and x5 has a correlation of 0.86. These correlation numbers are very high indicating a strong positive relationship between x4 and x2 and x4 and x5 respectively. Thus, the problem of multicollinearity exists in the model.

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Most popular questions from this chapter

Suppose you used Minitab to fit the model y=尾0+尾1x1+尾2x2+蔚

to n = 15 data points and obtained the printout shown below.

  1. What is the least squares prediction equation?

  2. Find R2and interpret its value.

  3. Is there sufficient evidence to indicate that the model is useful for predicting y? Conduct an F-test using 伪 = .05.

  4. Test the null hypothesis H0: 尾1= 0 against the alternative hypothesis Ha: 尾1鈮� 0. Test using 伪 = .05. Draw the appropriate conclusions.

  5. Find the standard deviation of the regression model and interpret it.

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?

Consider the following data that fit the quadratic modelE(y)=尾0+尾1x+尾2x2:

a. Construct a scatterplot for this data. Give the prediction equation and calculate R2based on the model above.

b. Interpret the value ofR2.

c. Justify whether the overall model is significant at the 1% significance level if the data result into a p-value of 0.000514.

Question: Shared leadership in airplane crews. Refer to the Human Factors (March 2014) study of shared leadership by the cockpit and cabin crews of a commercial airplane, Exercise 8.14 (p. 466). Recall that simulated flights were taken by 84 six-person crews, where each crew consisted of a 2-person cockpit (captain and first officer) and a 4-person cabin team (three flight attendants and a purser.) During the simulation, smoke appeared in the cabin and the reactions of the crew were monitored for teamwork. One key variable in the study was the team goal attainment score, measured on a 0 to 60-point scale. Multiple regression analysis was used to model team goal attainment (y) as a function of the independent variables job experience of purser (x1), job experience of head flight attendant (x2), gender of purser (x3), gender of head flight attendant (x4), leadership score of purser (x5), and leadership score of head flight attendant (x6).

a. Write a complete, first-order model for E(y) as a function of the six independent variables.

b. Consider a test of whether the leadership score of either the purser or the head flight attendant (or both) is statistically useful for predicting team goal attainment. Give the null and alternative hypotheses as well as the reduced model for this test.

c. The two models were fit to the data for the n = 60 successful cabin crews with the following results: R2 = .02 for reduced model, R2 = .25 for complete model. On the basis of this information only, give your opinion regarding the null hypothesis for successful cabin crews.

d. The p-value of the subset F-test for comparing the two models for successful cabin crews was reported in the article as p 6 .05. Formally test the null hypothesis using 伪 = .05. What do you conclude?

e. The two models were also fit to the data for the n = 24 unsuccessful cabin crews with the following results: R2 = .14 for reduced model, R2 = .15 for complete model. On the basis of this information only, give your opinion regarding the null hypothesis for unsuccessful cabin crews.

f. The p-value of the subset F-test for comparing the two models for unsuccessful cabin crews was reported in the article as p < .10. Formally test the null hypothesis using 伪 = .05. What do you conclude?
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