The following regression output was generated based on a sample of utility customers.The dependent variable was the dollar amount of the monthly bill and the independent variable was the size of the house in square feet. Based on this regression output,which of the following statements is not true?
A)The number of square feet in the house explains only about 2 percent of the variation in the monthly power bill.
B)At an alpha level equal to 0.05,there is no basis for rejecting the hypothesis that the slope coefficient is equal to zero.
C)The average increase in the monthly power bill is about 66.4 for each additional square foot of space in the house.
D)The correlation of the monthly power bill with the square footage of the house is 0.149

Question

The following regression output was generated based on a sample of utility customers.The dependent variable was the dollar amount of the monthly bill and the independent variable was the size of the house in square feet.  Based on this regression output,which of the following statements is not true?
A)The number of square feet in the house explains only about 2 percent of the variation in the monthly power bill. 
B)At an alpha level equal to 0.05,there is no basis for rejecting the hypothesis that the slope coefficient is equal to zero. 
C)The average increase in the monthly power bill is about 66.4 for each additional square foot of space in the house. 
D)The correlation of the monthly power bill with the square footage of the house is 0.149

Quizplus · Accepted Answer

Option A is true as the R-squared value of 0.022 indicates that only about 2 percent of the variation in the monthly power bill can be explained by the size of the house.

Option B is also true as the p-value for the size coefficient is 0.166, which is greater than the 0.05 significance level, indicating that we do not have sufficient evidence to reject the null hypothesis that the slope coefficient is equal to zero.

Option D is also true, as the correlation coefficient between the two variables is 0.149, as shown in the output.

Option C is not true, as the coefficient for the size variable is 0.0664, indicating that for every additional square foot of space in the house, the monthly power bill increases by $0.0664, not $66.4.

The Following Regression Output Was Generated Based on a Sample