/*! 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} 43E Reality TV and cosmetic surgery.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: 43E (page 739)

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 12.17 (p. 725). Recall that the data for the study (simulated based on statistics reported in the journal article) are saved in the file. Consider the interaction model, , where y = desire to have cosmetic surgery (25-point scale), = {1 if male, 0 if female}, and = impression of reality TV (7-point scale). The model was fit to the data and the resulting SPSS printout appears below.

a.Give the least squares prediction equation.

b.Find the predicted level of desire (y) for a male college student with an impression-of-reality-TV-scale score of 5.

c.Conduct a test of overall model adequacy. Use a= 0.10.

d.Give a practical interpretation of R2a.

e.Give a practical interpretation of s.

f.Conduct a test (at a = 0.10) to determine if gender (x1) and impression of reality TV show (x4) interact in the prediction of level of desire for cosmetic surgery (y).

Short Answer

Expert verified

a.The least-square prediction equation is E(y) =11.779-1.972x1+ 0.585x4+0.553 x1x4

b. The predicted score for a male student with an impression-of-reality-TV score of 5 is 9.967.

c.At 95% confidence interval, it can be concluded that尾1鈮�尾2鈮�尾3鈮�0 .

d.The value of adjusted R2 is 0.439 which indicates that the model is not a good fit for the data.

e. The value of s is 2.350 which is a lower value indicating that the data is close to the regression line plotted and that the data is not spr.

f.At 95% significance, 尾3= 0 .ead Hence it can be concluded with enough evidence that x1and x2do not interact in the model.

Step by step solution

01

Least square prediction equation

The least-square prediction equation is formed by substituting model parameters in the estimated equation. Here, the least square prediction equation isE(y) =11.779-1.972x1+ 0.585x4+0.553 x1x4

02

Finding prediction level of desire

Since the impression-of-reality-TV-scale score is 5, the value becomes 1 (since we want to predict the level of desire for a male college student). Therefore, mathematically

E(y) = 尾0+ 尾1x1+ 尾2x4 + 尾3x1x4


E(y) = 11.779- 1.972(1) + 0.585(5) -0.533(1) (5)

E(y)= 9.967

The predicted score for a male student with an impression-of-reality-TV score of 5 is 9.967.

03

Significance of the model

H0: 尾1 =尾2 = 尾3= 0

Ha : at least one of the parameters localid="1649922695702" 尾1 ,尾尾2,尾3 is non zero

Here, F test statistic =SSE/n-(k-1) = 916.787/393-4 = 2.356

Value of F0.05389389 is 1

H0is rejected if F statistic > F0.05389389

For a= 0.05, since F > F0.05389389 Sufficient evidence to reject H0 at 95% confidence interval.

04

Interpretation of R2 a

Adjusted R2denoted by R2a explains the variation in the variables which is explained by the model when additional independent variables are added in the model. The high value of R2a indicates that the model is a good fit for the data while a lower value denotes that the model is not a good fit for the data. Here the value of adjusted R2 is 0.439 which indicates that the model is not a good fit for the data.

05

Analysis of s

The standard error of the regression (s) measures the distance of the data points from the regression line. It gives an estimate of the spread of the data points. Higher value denotes that the data is spread while lower value denotes the data points are closer to the regression line meaning the regression line is a good fit of the data. Here, the value of s is 2.350 which is a lower value indicating that the data is close to the regression line plotted and that the data is not spread.

06

Importance ofβ

H0: 尾3=0

H0: 尾鈮�0

Here, t-test statistic= 0.0536/0.276 = -0.2039

Value of t0.05374 is 1.645 H0is rejected if t is statistic >t0.05374. For a=0.05 since t >t0.05374. Not sufficient evidence to reject H0at a 95% confidence interval.

Thus, 尾=0 .Hence it can be concluded with enough evidence that x1and x2 do not interact 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: 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.


Factors that impact an auditor鈥檚 judgment. A study was conducted to determine the effects of linguistic delivery style and client credibility on auditors鈥� 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鈥檚 financial statement. The researchers gave the auditors different information on the client鈥檚 credibility and linguistic delivery style of the client鈥檚 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鈥攃redibility (x1), linguistic delivery style (x2) , and likelihood (y) 鈥攚ere all measured on a numerical scale. Regression analysis was used to fit the interaction model,y=尾0+尾1x1+尾2x2+尾3x1x2+蔚 . 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鈥搇inguistic 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鈥搇inguistic 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: Diet of ducks bred for broiling. Corn is high in starch content; consequently, it is considered excellent feed for domestic chickens. Does corn possess the same potential in feeding ducks bred for broiling? This was the subject of research published in Animal Feed Science and Technology (April 2010). The objective of the study was to establish a prediction model for the true metabolizable energy (TME) of corn regurgitated from ducks. The researchers considered 11 potential predictors of TME: dry matter (DM), crude protein (CP), ether extract (EE), ash (ASH), crude fiber (CF), neutral detergent fiber (NDF), acid detergent fiber (ADF), gross energy (GE), amylose (AM), amylopectin (AP), and amylopectin/amylose (AMAP). Stepwise regression was used to find the best subset of predictors. The final stepwise model yielded the following results:

TME^=7.70+2.14(AMAP)+0.16(NDF), R2 = 0.988, s = .07, Global F p-value = .001

a. Determine the number of t-tests performed in step 1 of the stepwise regression.

b. Determine the number of t-tests performed in step 2 of the stepwise regression.

c. Give a full interpretation of the final stepwise model regression results.

d. Explain why it is dangerous to use the final stepwise model as the 鈥渂est鈥� model for predicting TME.

e. Using the independent variables selected by the stepwise routine, write a complete second-order model for TME.

f. Refer to part e. How would you determine if the terms in the model that allow for curvature are statistically useful for predicting TME?

Question: There are six independent variables, x1, x2, x3, x4, x5, and x6, that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The software fits all possible one-variable models of the form

where xi is the ith independent variable, i = 1, 2, 鈥�, 6. The information in the table is provided from the computer printout.

E(Y)=尾0+尾1xi

a. Which independent variable is declared the best one variable predictor of y? Explain.

b. Would this variable be included in the model at this stage? Explain.

c. Describe the next phase that a stepwise procedure would execute.

Question: Glass as a waste encapsulant. Because glass is not subject to radiation damage, encapsulation of waste in glass is considered to be one of the most promising solutions to the problem of low-level nuclear waste in the environment. However, chemical reactions may weaken the glass. This concern led to a study undertaken jointly by the Department of Materials Science and Engineering at the University of Florida and the U.S. Department of Energy to assess the utility of glass as a waste encapsulant. Corrosive chemical solutions (called corrosion baths) were prepared and applied directly to glass samples containing one of three types of waste (TDS-3A, FE, and AL); the chemical reactions were observed over time. A few of the key variables measured were

y = Amount of silicon (in parts per million) found in solution at end of experiment. (This is both a measure of the degree of breakdown in the glass and a proxy for the amount of radioactive species released into the environment.)

x1 = Temperature (掳C) of the corrosion bath

x2 = 1 if waste type TDS-3A, 0 if not

x3 = 1 if waste type FE, 0 if not

(Waste type AL is the base level.) Suppose we want to model amount y of silicon as a function of temperature (x1) and type of waste (x2, x3).

a. Write a model that proposes parallel straight-line relationships between amount of silicon and temperature, one line for each of the three waste types.

b. Add terms for the interaction between temperature and waste type to the model of part a.

c. Refer to the model of part b. For each waste type, give the slope of the line relating amount of silicon to temperature.

e. Explain how you could test for the presence of temperature鈥搘aste type interaction.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.