/*! 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} Q120E Question: Identify the problem(s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q120E (page 803)

Question: Identify the problem(s) in each of the residual plots shown below.

Short Answer

Expert verified

Answer

a. The mean of residual is not equal to 0 here. Plot of the residuals for the straight-line model reveals a nonrandom pattern. The residuals exhibit a curved shape. The indication is that the mean value of the random error, within the ranges of x (small, medium, large) may not be equal to 0. Such a pattern usually indicates that curvature needs to be added to the model.

b. The variance of the error is not constant which can be seen in the graph. The range in values of the residuals increases as y increases, thus indicating that the variance of the random error becomes larger as the estimate of E(y) increases in value.

c. The residuals appear to be randomly distributed around the 0 line. However, the residuals seem to be between +/- 3s range which indicates that the model is good fit for the data.

d. The error terms should be normally distributed. But, from the graph it is visible that the error terms are not normally distributed. It appears to be a positively distributed data.

Step by step solution

01

Problem in graph a 

The mean of residual is not equal to 0 here. Plot of the residuals for the straight-line model reveals a nonrandom pattern. The residuals exhibit a curved shape. The indication is that the mean value of the random error, within the ranges of x (small, medium, large) may not be equal to 0. Such a pattern usually indicates that curvature needs to be added to the model.

02

Problem in graph b

The variance of the error is not constant which can be seen in the graph. The range in values of the residuals increases as y increases, thus indicating that the variance of the random error becomes larger as the estimate of E(y) increases in value.

03

Problem in graph c

The residuals appear to be randomly distributed around the 0 line. However, the residuals seem to be between +/- 3s range which indicates that the model is good fit for the data.

04

Problem in graph d

The error terms should be normally distributed. But, from the graph it is visible that the error terms are not normally distributed. It appears to be a positively distributed data.

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: 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

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

Question: Manipulating rates of return with stock splits. Some firms have been accused of using stock splits to manipulate their stock prices before being acquired by another firm. An article in Financial Management (Winter 2008) investigated the impact of stock splits on long-run stock performance for acquiring firms. A simplified version of the model fit by the researchers follows:

E(y)=尾0+尾1x1+尾2x2+尾3x1x2

where

y = Firm鈥檚 3-year buy-and-hold return rate (%)

x1 = {1 if stock split prior to acquisition, 0 if not}

x2 = {1 if firm鈥檚 discretionary accrual is high, 0 if discretionary accrual is low}

a. In terms of the 尾鈥檚 in the model, what is the mean buy and- hold return rate (BAR) for a firm with no stock split and a high discretionary accrual (DA)?

b. In terms of the 尾鈥檚 in the model, what is the mean BAR for a firm with no stock split and a low DA?

c. For firms with no stock split, find the difference between the mean BAR for firms with high and low DA. (Hint: Use your answers to parts a and b.)

d. Repeat part c for firms with a stock split.

e. Note that the differences, parts c and d, are not the same. Explain why this illustrates the notion of interaction between x1 and x2.

f. A test for H0: 尾3 = 0 yielded a p-value of 0.027. Using 伪 = .05, interpret this result.

g. The researchers reported that the estimated values of both 尾2 and 尾3 are negative. Consequently, they conclude that 鈥渉igh-DA acquirers perform worse compared with low-DA acquirers. Moreover, the underperformance is even greater if high-DA acquirers have a stock split before acquisition.鈥� Do you agree?

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: Women in top management. Refer to the Journal of Organizational Culture, Communications and Conflict (July 2007) study on women in upper management positions at U.S. firms, Exercise 11.73 (p. 679). Monthly data (n = 252 months) were collected for several variables in an attempt to model the number of females in managerial positions (y). The independent variables included the number of females with a college degree (x1), the number of female high school graduates with no college degree (x2), the number of males in managerial positions (x3), the number of males with a college degree (x4), and the number of male high school graduates with no college degree (x5). The correlations provided in Exercise 11.67 are given in each part. Determine which of the correlations results in a potential multicollinearity problem for the regression analysis.

  1. The correlation relating number of females in managerial positions and number of females with a college degree: r =0.983.

  2. The correlation relating number of females in managerial positions and number of female high school graduates with no college degree: r =0.074.

  3. The correlation relating number of males in managerial positions and number of males with a college degree: r =0.722.

  4. The correlation relating number of males in managerial positions and number of male high school graduates with no college degree: r =0.528.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Decision 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.