What are the factors that determine the acceleration time (in sec.) from 0 to 60
ID: 3220425 • Letter: W
Question
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 30 different vehicle models were collected:
Y (Accel Time): Acceleration time in sec.
X1 (Engine Size): c.c.
X2 (Sedan): 1 if the vehicle model is a sedan and 0 otherwise
The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below.
The coefficient of partial determination r 2 Y1.2 and r 2 Y2.1 are 0.3301, and 0.0594, respectively. The coefficient of determination for the regression model using each of the 2 independent variables as the dependent variable and the other independent variable as independent variables ( R 2 j ) are, respectively 0.0077, and 0.0077.
Q1) What is the correct interpretation for the estimated coefficient for X1?
A) As the 0 to 60 miles per hour acceleration time increases by one second, the mean engine size will decrease by an estimated 0.0005 c.c. without taking into consideration the other independent variable included in the model
B) As the 0 to 60 miles per hour acceleration time increases by one second, the mean engine size will decrease by an estimated 0.0005 c.c. taking into consideration the other independent variable included in the model
C) As the engine size increases by one c.c., the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0005 seconds without taking into consideration the other independent variable included in the model
D) As the engine size increases by one c.c., the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0005 seconds taking into consideration the other independent variable included in the model.
Q2) What is the correct interpretation for the estimated coefficient for X2?
A) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds lower than that of a non-sedan after considering the effect of the engine size
B) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds higher than that of a non-sedan without considering the effect of the engine size
C) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds higher than that of a non-sedan after considering the effect of the engine size
D) The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds lower than that of a non-sedan without considering the effect of the engine size.
Regression Statistics Multiple R 0.6096 0.3716 R Square Adjusted Rsquare 0.3251 Standard Error 1.4629 Observations ANOVA MS SS F Significance F 34.1744 17.0872 7.9839 0.0019 Regression Residual 57.7856 2.1402 Total 29 91.9600 Coefficients Standard Error t Stat P-value Lower 95% upper 95% 0.6574 10.8086 0.0000 7.1052 5.7564 8.4540 Intercept Engine Size -0.0005 0.0001 3.6477 0.0011 -0.0008 0.0002. -0.4152 1.8681 0.5564 1.3056 0.2027 Sedan 0.7264Explanation / Answer
Ans - 1: Correct interpretation for the estimated coefficient for X1:
As the engine size increases by one c.c., the mean 0 to 60 miles per hour acceleration time will decrease by an estimated 0.0005 seconds without taking into consideration the other independent variable included in the model
Option C is correct.
Ans - 2: Correct interpretation for the estimated coefficient for X2:
The mean 0 to 60 miles per hour acceleration time of a sedan is estimated to be 0.7264 seconds higher than that of a non-sedan without considering the effect of the engine size.
Option B is correct.
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