Question

Amelia used a random sample of 100 accounts receivable to estimate the relationship between Days (number of days from billing to receipt of payment) and Size (size of balance due in dollars). Her estimated regression equation was Days = 22 + 0.0047 size with a correlation coefficient of .300. from this information we can conclude that:

A) 9 percent of the variation in Days is explained by Size.
B) autocorrelation is likely to be a problem.
C) the relationship between Days and Size is significant.
D) larger accounts usually take less time to pay.

Answer 1

A) 9 percent of the variation in Days is explained by Size.

Explanation:

A) 9 percent of the variation in Days is explained by Size.

r ², the coefficient of determination, which is the correlation between the dependent variable and the set of independent variables.

So since r = correlation coefficient= 0.3, therefore so r ² = 0.09 =9%

Therefore, 9% of the variation in Days can be explained by Size.

B) autocorrelation is likely to be a problem.

This is not possible.

C) the relationship between Days and Size is significant.

To have a significant relationship the value of r ² between 0 and 1 needs to be close to 1. r ² = 9% is closer to 0 and this indicates the regression model does not fit the data well.

D) larger accounts usually take less time to pay.

This is incorrect as relationship is a positive relationship which means more size tend to more days.

9 percent of the variation in Days is explained by Size is therefore the only conclusion we can get from the information.