Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q119E (page 782)

Question: After-death album sales. When a popular music artist dies, sales of the artist’s albums often increase dramatically. A study of the effect of after-death publicity on album sales was published in Marketing Letters (March 2016). The following data were collected weekly for each of 446 albums of artists who died a natural death: album publicity (measured as the total number of printed articles in which the album was mentioned at least once during the week), artist death status (before or after death), and album sales (dollars). Suppose you want to use the data to model weekly album sales (y) as a function of album publicity and artist death status. Do you recommend using stepwise regression to find the “best” model for predicting y? Explain. If not, outline a strategy for finding the best model.

Short Answer

Expert verified

Answer

Stepwise regression model is used when there are a lot of independent variables to consider for explaining the dependent variable. In this case, there are only 2 independent variables: album publicity and artist death status. Using stepwise regression would be time consuming and inefficient.

The significance of the model can be tested using an F-test and individual t-test for individual β parameters.

Step by step solution

01

Stepwise regression

Stepwise regression model is used when there are a lot of independent variables to consider for explaining the dependent variable. In this case, there are only 2 independent variables: album publicity and artist death status. Using stepwise regression would be time consuming and inefficient.

02

 Step 2: Best model for the data

The significance of the model can be tested using an F-test and individual t-test for individual β parameters.

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: Suppose you fit the regression modelE(y)=β0+β1x1+β2x2+β3x1+β4x12+β5x22to n = 30 data points and wish to test H0: β3 = β4 = β5 = 0

a. State the alternative hypothesis Ha.

b. Give the reduced model appropriate for conducting the test.

c. What are the numerator and denominator degrees of freedom associated with the F-statistic?

d. Suppose the SSE’s for the reduced and complete models are SSER = 1,250.2 and SSEC = 1,125.2. Conduct the hypothesis test and interpret the results of your test. Test using α = .05.

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 “best” 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: Suppose you fit the first-order multiple regression model y=β0+β1x1+β2x2+ε to n=25 data points and obtain the prediction equationy^=6.4+3.1x1+0.92x2 . The estimated standard deviations of the sampling distributions of β1 and β2are 2.3 and .27, respectively

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.

Catalytic converters in cars. A quadratic model was applied to motor vehicle toxic emissions data collected in Mexico City (Environmental Science & Engineering, Sept. 1, 2000). The following equation was used to predict the percentage (y) of motor vehicles without catalytic converters in the Mexico City fleet for a given year (x): β^2

a. Explain why the valueβ^0=325790has no practical interpretation.

b. Explain why the valueβ^1=-321.67should not be Interpreted as a slope.

c. Examine the value ofβ^2to determine the nature of the curvature (upward or downward) in the sample data.

d. The researchers used the model to estimate “that just after the year 2021 the fleet of cars with catalytic converters will completely disappear.” Comment on the danger of using the model to predict y in the year 2021. (Note: The model was fit to data collected between 1984 and 1999.)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and 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.

Sign-up for free