Chapter 29, Problem 29.31CYS

To determine

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

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:

$x_1=\text{Mph}$

$x_2=\text{Incline}$

$x_3=\text{IndSlow as 1 if Mph}\le 3\text{, IndSlow as 0 if Mph}>3$

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

${\beta }_0$ is the intercept term.

${\beta }_1$ is the effect due to Mph.

${\beta }_2$ is the effect due to Incline.

${\beta }_3$ is the effect due to indicator variable $x_3$.

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 $x_1,x_2,\mathrm{...},x_p$ and a response variable y. The general form of multiple linear regression model is given below:

${\mu }_y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\mathrm{...}{\beta }_p{x}_p,$

Where, ${\mu }_y$ is the mean response and $\beta \text{'}\text{s}$ are the unknown parameters.