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Chapter 12: Q.97E (page 772)

Question: Determine which pairs of the following models are 鈥渘ested鈥� models. For each pair of nested models, identify the complete and reduced model.

a.E(y)=尾0+尾1x1+尾2x2b.E(y)=尾0+尾1x1c.E(y)=尾0+尾1x1+尾2x12d.E(y)=尾0+尾1x1+尾2x2+尾3x1x2e.E(y)=尾0+尾1x1+尾2x2+尾3x1x2+尾4x21+尾5x22


Short Answer

Expert verified

Answer

a. Option a is a nested model in two variables for option d and option e.

b. Option b is a nested model for all of the options.

c. Option c is a nested model for option e and a complete model for option b.

d. Option d is a nested model for option e and a complete model for option a.

e. Option e is a complete model for all of the options.

Step by step solution

01

Nested models 

Option a is a nested model in two variables for option d and option e.

02

Fixed Representation 

Option b is a nested model for all of the options.

03

Enclosed reproduction

Option c is a nested model for option e and a complete model for option b.

04

Ingrained Imitation

Option d is a nested model for option e and a complete model for option a.

05

Impacted duplicate

Option e is a complete model for all of the options.

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Most popular questions from this chapter

Question: Tilting in online poker. In poker, making bad decisions due to negative emotions is known as tilting. A study in the Journal of Gambling Studies (March, 2014) investigated the factors that affect the severity of tilting for online poker players. A survey of 214 online poker players produced data on the dependent variable, severity of tilting (y), measured on a 30-point scale (where higher values indicate a higher severity of tilting). Two independent variables measured were poker experience (x1, measured on a 30-point scale) and perceived effect of experience on tilting (x2, measured on a 28-point scale). The researchers fit the interaction model, . The results are shown below (p-values in parentheses).

  1. Evaluate the overall adequacy of the model using 伪 = .01.

b. The researchers hypothesize that the rate of change of severity of tilting (y) with perceived effect of experience on tilting (x2) depends on poker experience (x1). Do you agree? Test using 伪 = .01.

Question: Suppose the mean value E(y) of a response y is related to the quantitative independent variables x1and x2

E(y)=2+x1-3x2-x1x2

a. Identify and interpret the slope forx2.

b. Plot the linear relationship between E(y) andx2forx1=0,1,2, where.

c. How would you interpret the estimated slopes?

d. Use the lines you plotted in part b to determine the changes in E(y) for each x1=0,1,2.

e. Use your graph from part b to determine how much E(y) changes when3猢�x1猢�5and1猢�x2猢�3.

Question: Suppose you fit the regression modelE(y)=尾0+尾1x1+尾2x2+尾3x1+尾4x12+尾5x22to n = 30 data points and wish to test H0: 尾3 = 尾4 = 尾5 = 0

a. State the alternative hypothesis Ha.

b. Give the reduced model appropriate for conducting the test.

c. What are the numerator and denominator degrees of freedom associated with the F-statistic?

d. Suppose the SSE鈥檚 for the reduced and complete models are SSER = 1,250.2 and SSEC = 1,125.2. Conduct the hypothesis test and interpret the results of your test. Test using 伪 = .05.

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

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.
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