Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q140SE (page 807)

It is desired to relate E(y) to a quantitative variable x1and a qualitative variable at three levels.

  1. Write a first-order model.

  2. Write a model that will graph as three different second- order curves—one for each level of the qualitative variable.

Short Answer

Expert verified

  1. A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written asEy=β0+β1x1+β2x2+β3x3

  2. Graph

Step by step solution

01

First-order model

A first-order model equation in one quantitative variable and one qualitative variable with 3 levels can be written asE(y)=β0+β1x1+β2x2+β3x3

Where x1is the quantitative variable

And x2 and x3 represent level 1 and level 2 of the qualitative variable.

02

Graph

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

Explain why stepwise regression is used. What is its value in the model-building process?

Production technologies, terroir, and quality of Bordeaux wine. In addition to state-of-the-art technologies, the production of quality wine is strongly influenced by the natural endowments of the grape-growing region—called the “terroir.” The Economic Journal (May 2008) published an empirical study of the factors that yield a quality Bordeaux wine. A quantitative measure of wine quality (y) was modeled as a function of several qualitative independent variables, including grape-picking method (manual or automated), soil type (clay, gravel, or sand), and slope orientation (east, south, west, southeast, or southwest).

  1. Create the appropriate dummy variables for each of the qualitative independent variables.
  2. Write a model for wine quality (y) as a function of grape-picking method. Interpret theβ’s in the model.
  3. Write a model for wine quality (y) as a function of soil type. Interpret theβ’s in the model.
  4. Write a model for wine quality (y) as a function of slope orientation. Interpret theβ’s in the model.

Question: Write a regression model relating the mean value of y to a qualitative independent variable that can assume two levels. Interpret all the terms in the model.

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.

Question:How is the number of degrees of freedom available for estimating σ2(the variance ofε ) related to the number of independent variables in a regression model?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

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