Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: 134SE (page 807)

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 ≤ y ≤ 100, 5 ≤ x1 ≤ 55, 0.5 ≤ x2 ≤ 1, and 1,000 ≤ x3 ≤ 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?

Short Answer

Expert verified

Therefore, when predicting y values, the error of prediction will be smaller when x1= 30, x2 = 0.6, and x3 = 1300 since the values of independent variables are well within the range described in the question.

Step by step solution

01

Range of independent variables

The range of x1, x2, and x3 is given as 5 ≤ x1 ≤ 55, 0.5 ≤ x2 ≤ 1, and 1,000 ≤ x3 ≤ 2,000. When x1= 30, x2 = 0.6, and x3 = 1300, all the variables x1,x2 and x3are well within the range of values. While when x1 = 60, x2 = 0.4, and x3 = 900, x1and x2 are out of the range and x3 is within the range.

02

Conclusion

Therefore, when predicting y values, the error of prediction will be smaller when x1= 30, x2 = 0.6, and x3 = 1300.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Question: Determine which pairs of the following models are “nested” models. For each pair of nested models, identify the complete and reduced model.

a.E(y)=β0+β1x1+β2x2b.E(y)=β0+β1x1c.E(y)=β0+β1x1+β2x12d.E(y)=β0+β1x1+β2x2+β3x1x2e.E(y)=β0+β1x1+β2x2+β3x1x2+β4x21+β5x22

Question: Workplace bullying and intention to leave. Workplace bullying has been shown to have a negative psychological effect on victims, often leading the victim to quit or resign. In Human Resource Management Journal (October 2008), researchers employed multiple regression to examine whether perceived organizational support (POS) would moderate the relationship between workplace bullying and victims’ intention to leave the firm. The dependent variable in the analysis, intention to leave (y), was measured on a quantitative scale. The two key independent variables in the study were bullying (, measured on a quantitative scale) and perceived organizational support (measured qualitatively as “low,” “neutral,” or “high”).

  1. Set up the dummy variables required to represent POS in the regression model.
  2. Write a model for E(y) as a function of bullying and POS that hypothesizes three parallel straight lines, one for each level of POS.
  3. Write a model for E(y) as a function of bullying and POS that hypothesizes three non-parallel straight lines, one for each level of POS.
  4. The researchers discovered that the effect of bullying on intention to leave was greater at the low level of POS than at the high level of POS. Which of the two models, parts b and c, support these findings?

Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to forecast movie box office revenue, Exercise 12.10 (p. 723). The researchers modelled a movie’s opening weekend box office revenue (y) as a function of tweet rate (x1 ) and ratio of positive to negative tweets (x2) using a first-order model.

a) Write the equation of an interaction model for E(y) as a function of x1 and x2 .

b) In terms of theβ in the model, part a, what is the change in revenue (y) for every 1-tweet increase in the tweet rate (x1 ) , holding PN-ratio (x2)constant at a value of 2.5?

c) In terms of the in the model, part a, what is the change in revenue (y) for every 1-tweet increase in the tweet rate (x1 ) , holding PN-ratio (x2)constant at a value of 5.0?

d) In terms of theβ in the model, part a, what is the change in revenue (y) for every 1-unit increase in the PN-ratio (x2) , holding tweet rate (x1 )constant at a value of 100?

e) Give the null hypothesis for testing whether tweet rate (x1 ) and PN-ratio (x2) interact to affect revenue (y).


Factors that impact an auditor’s judgment. A study was conducted to determine the effects of linguistic delivery style and client credibility on auditors’ judgments (Advances in Accounting and Behavioural Research, 2004). Two hundred auditors from Big 5 accounting firms were each asked to perform an analytical review of a fictitious client’s financial statement. The researchers gave the auditors different information on the client’s credibility and linguistic delivery style of the client’s explanation. Each auditor then provided an assessment of the likelihood that the client-provided explanation accounted for the fluctuation in the financial statement. The three variables of interest—credibility (x1), linguistic delivery style (x2) , and likelihood (y) —were all measured on a numerical scale. Regression analysis was used to fit the interaction model,y=β0+β1x1+β2x2+β3x1x2+ε . The results are summarized in the table at the bottom of page.

a) Interpret the phrase client credibility and linguistic delivery style interact in the words of the problem.

b) Give the null and alternative hypotheses for testing the overall adequacy of the model.

c) Conduct the test, part b, using the information in the table.

d) Give the null and alternative hypotheses for testing whether client credibility and linguistic delivery style interact.

e) Conduct the test, part d, using the information in the table.

f) The researchers estimated the slope of the likelihood–linguistic delivery style line at a low level of client credibility 1x1 = 222. Obtain this estimate and interpret it in the words of the problem.

g) The researchers also estimated the slope of the likelihood–linguistic delivery style line at a high level of client credibility 1x1 = 462. Obtain this estimate and interpret it in the words of the problem.

Question: Personality traits and job performance. Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.54 (p. 747). Recall that the researchers used a quadratic model to relate y = task performance score (measured on a 30-point scale) to x1 = conscientiousness score (measured on a scale of -3 to +3). In addition, the researchers included job complexity in the model, where x2 = {1 if highly complex job, 0 if not}. The complete model took the form

E(y)=β0+β1x1+β2x12+β3x2+β4x1x2+β5x12x2herex2=1E(y)=β0+β1x1+β2x12+β3(1)+β4x1(1)+β5(1)2(1)E(y)=(β0+β3)+(β1+β4)x1+(β2+β5)(x1)2

a. For jobs that are not highly complex, write the equation of the model for E1y2 as a function of x1. (Substitute x2 = 0 into the equation.)

b. Refer to part a. What do each of the b’s represent in the model?

c. For highly complex jobs, write the equation of the model for E(y) as a function of x1. (Substitute x2 = 1 into the equation.)

d. Refer to part c. What do each of the b’s represent in the model?

e. Does the model support the researchers’ theory that the curvilinear relationship between task performance score (y) and conscientiousness score (x1) depends on job complexity (x2)? Explain.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free