Loose-leaf Version for The Basic Practice of Statistics 7e & LaunchPad (Twelve Month Access)
Loose-leaf Version for The Basic Practice of Statistics 7e & LaunchPad (Twelve Month Access)
7th Edition
ISBN: 9781319019334
Author: David S. Moore, William I. Notz, Michael A. Fligner
Publisher: W. H. Freeman
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Question
Chapter 29, Problem 29.31CYS
To determine

To identify: The number of parameters in the given multiple regression model.

Expert Solution & Answer
Check Mark

Answer to Problem 29.31CYS

Correct answer:

Option (a): 4.

Explanation of Solution

Reason for correct answer:

The problem deals with the treadmill display showing the calories per hour by speed for a 175-pound male who is running on a Cybex treadmill, and it is inclined at 0%, 2%, and 4%.

The explanatory variables are given below:

x1=Mph

x2=Incline

x3=IndSlow as 1 if Mph3, IndSlow as 0 if Mph>3

The parameters used in the given problem are 4, which is defined as follows:

β0 is the intercept term.

β1 is the effect due to Mph.

β2 is the effect due to Incline.

β3 is the effect due to indicator variable x3 .

Thus, there are 4 parameters in the given multiple regression model.

Reason for incorrect answers:

Option (b): 5.

The given options suggest that there are 5 parameters in the given regression model.

By using the theory of multiple regression, it is identified that there are only 4 parameters given in the model. Thus, the given option is incorrect.

Option (c): 6

The given option suggest that there are 6 parameters in the given regression model.

By using the theory of multiple regression, it is identified that there are only 4 parameters given in the model. Thus, the given option is incorrect.

Thus, the options (b) and (c) are incorrect.

Conclusion:

Thus, there are 4 parameters in the given multiple regression model.

Statistics Concept Introduction

Introduction:

Multiple Linear Regression:

Consider the number of observation on n individuals for which each observation has p explanatory variables x1,x2,...,xp and a response variable y. The general form of multiple linear regression model is given below:

μy=β0+β1x1+β2x2+...βpxp,

Where, μy is the mean response and β's are the unknown parameters.

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