/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: 138SE (page 807)

The first-order model E(y)=尾0+尾1x1was fit to n = 19 data points. A residual plot for the model is provided below. Is the need for a quadratic term in the model evident from the residual plot? Explain.

Short Answer

Expert verified

The residual plot indicates a strong positive relation among dependent and independent variable. And since the residual points are clustered around in a straight line, the graph is indicating a linear relationship among y and x. Since the graph indicates a linear relationship between dependent and independent variable, there is no need for an additional quadratic term in the model.

Step by step solution

01

Residual plot

The residual plot indicates a strong positive relation among dependent and independent variable. And since the residual points are clustered around in a straight line, the graph is indicating a linear relationship among y and x.

02

Need for quadratic term

Since the graph indicates a linear relationship between dependent and independent variable, there is no need for an additional quadratic term in the model.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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: Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (March 2010) study of the impact of reality TV shows on a college student鈥檚 decision to undergo cosmetic surgery, Exercise 12.43 (p. 739). The data saved in the file were used to fit the interaction model, E(Y)=尾0+尾1x1+尾2x4+尾3x1x4, where y = desire to have cosmetic surgery (25-point scale),x1= {1 if male, 0 if female}, and x4= impression of reality TV (7-point scale). From the SPSS printout (p. 739), the estimated equation is:y^=11.78-1.97x1+0.58x4-0.55x1x4

a. Give an estimate of the change in desire (y) for every 1-point increase in impression of reality TV show (x4) for female students.

b. Repeat part a for male students.

Question: Job performance under time pressure. Time pressure is common at firms that must meet hard and fast deadlines. How do employees working in teams perform when they perceive time pressure? And, can this performance improve with a strong team leader? These were the research questions of interest in a study published in the Academy of Management Journal (October, 2015). Data were collected on n = 139 project teams working for a software company in India. Among the many variables recorded were team performance (y, measured on a 7-point scale), perceived time pressure (, measured on a 7-point scale), and whether or not the team had a strong and effective team leader (x2 = 1 if yes, 0 if no). The researchers hypothesized a curvilinear relationship between team performance (y) and perceived time pressure (), with different-shaped curves depending on whether or not the team had an effective leader (x2). A model for E(y) that supports this theory is the complete second-order model:E(y)=尾0+尾1x1+尾2x12+尾3x2+尾4x1x2+尾5x12x2

a. Write the equation for E(y) as a function of x1 when the team leader is not effective (x2= 0).

b. Write the equation for E(y) as a function ofwhen the team leader is effective (x2= 1).

c. The researchers reported the following b-estimates:.

尾0^=4.5,尾1^=0.13,尾3^=0.15,尾4^=0.15and尾5^=0.29Use these estimates to sketch the two equations, parts a and b. What is the nature of the curvilinear relationship when the team leaders is not effective? Effective?

Question: Suppose you fit the interaction model y=尾0+尾1x1+尾2x2+尾3x1x2+蔚 to n = 32 data points and obtain the following results:SSyy=479,鈥�SSE=21,鈥�尾^3=10, and s尾^3=4

a. Find R2and interpret its value.

b. Is the model adequate for predicting y? Test at 伪=.05

c. Use a graph to explain the contribution of the x1 , x2 term to the model.

d. Is there evidence that x1and x2 interact? Test at 伪=.05 .

Question: Revenues of popular movies. The Internet Movie Database (www.imdb.com) monitors the gross revenues for all major motion pictures. The table on the next page gives both the domestic (United States and Canada) and international gross revenues for a sample of 25 popular movies.

  1. Write a first-order model for foreign gross revenues (y) as a function of domestic gross revenues (x).
  2. Write a second-order model for international gross revenues y as a function of domestic gross revenues x.
  3. Construct a scatterplot for these data. Which of the models from parts a and b appears to be the better choice for explaining the variation in foreign gross revenues?
  4. Fit the model of part b to the data and investigate its usefulness. Is there evidence of a curvilinear relationship between international and domestic gross revenues? Try using伪=0.05.
  5. Based on your analysis in part d, which of the models from parts a and b better explains the variation in international gross revenues? Compare your answer with your preliminary conclusion from part c.

To model the relationship between y, a dependent variable, and x, an independent variable, a researcher has taken one measurement on y at each of three different x-values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order model Ey=尾0+尾1x+尾2x2 and it will pass exactly through all three points, yielding SSE = 0. The researcher, delighted with the excellent fit of the model, eagerly sets out to use it to make inferences. What problems will he encounter in attempting to make inferences?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Geometry

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.