SCENARIO 18-9
What are the factors that determine the acceleration time (in sec. )from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu.ft.
HP: Horsepower MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
The various residual plots are as shown below.

The coefficient of partial determination ( R 2 yj.(All variables except j ) )of each of the 5 predictors are, respectively,0.0380,0.4376,0.0248,0.0188,and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables X j as the dependent variable and all other X variables as independent variables ( R 2 j )are,respectively, 0.7461,0.5676,0.6764,0.8582,0.6632.
-Referring to Scenario 18-9,what is the correct interpretation for the estimated coefficient for Cargo Vol?
A)As the 0 to 60 miles per hour acceleration time increases by one second,the mean cargo volume will increase by an estimated 0.0259 cubic foot without taking into consideration all the other independent variables included in the model.
B)As the cargo volume increases by one cubic foot,the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds without taking into consideration all the other independent variables included in the model.
C)As the 0 to 60 miles per hour acceleration time increases by one second,the mean cargo volume will increase by an estimated 0.0259 cubic foot taking into consideration all the other independent variables included in the model.
D)As the cargo volume increases by one cubic foot,the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds taking into consideration all the other independent variables included in the model.

Question

SCENARIO 18-9
What are the factors that determine the acceleration time (in sec. )from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected:
Accel Time: Acceleration time in sec.
Cargo Vol: Cargo volume in cu.ft.
HP: Horsepower MPG: Miles per gallon
SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
  The various residual plots are as shown below.  
   
    The coefficient of partial determination ( R 2 yj.(All variables except j ) )of each of the 5 predictors are, respectively,0.0380,0.4376,0.0248,0.0188,and 0.0312.
The coefficient of multiple determination for the regression model using each of the 5 variables X j as the dependent variable and all other X variables as independent variables ( R 2 j )are,respectively, 0.7461,0.5676,0.6764,0.8582,0.6632.
-Referring to Scenario 18-9,what is the correct interpretation for the estimated coefficient for Cargo Vol?
A)As the 0 to 60 miles per hour acceleration time increases by one second,the mean cargo volume will increase by an estimated 0.0259 cubic foot without taking into consideration all the other independent variables included in the model. 
B)As the cargo volume increases by one cubic foot,the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds without taking into consideration all the other independent variables included in the model. 
C)As the 0 to 60 miles per hour acceleration time increases by one second,the mean cargo volume will increase by an estimated 0.0259 cubic foot taking into consideration all the other independent variables included in the model. 
D)As the cargo volume increases by one cubic foot,the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds taking into consideration all the other independent variables included in the model.

Quizplus · Accepted Answer

The correct interpretation of a coefficient in a regression model is about the relationship between the independent variable (in this case, Cargo Vol) and the dependent variable, while controlling for or holding constant the other variables in the model. Therefore, choice D correctly states that as the cargo volume increases by one cubic foot, the mean 0 to 60 miles per hour acceleration time will increase by an estimated 0.0259 seconds, considering the effects of all other variables in the model.

SCENARIO 18-9 What Are the Factors That Determine the Acceleration Time (In