Kilbaha 2009 exam

[Studyinghard]

If, for a sample of students, 85% of the variation in the hours they spent doing homework can be explained by the variation in the hours they spent watching television, then which one of the following statements must be true?
A.   A strong positive correlation exists between the two variables.
B.   Pearson’s correlation coefficient must be greater than 0.85
C.   The least squares regression line has a negative gradient
D.   The slope of the least squares regression line is 0.92
E.   Time spent watching television is the independent variable.

I said C. But answer is E.
?

[onerealsmartass]

yea E is right. because the coefiiciesnt of determination tells us that ___% of the variation in the dependent variable can be explained by the variaiton in the independent variable

[sam.utute]

If, for a sample of students, 85% of the variation in the hours they spent doing homework can be explained by the variation in the hours they spent watching television, then which one of the following statements must be true?
A.   A strong positive correlation exists between the two variables.
B.   Pearson’s correlation coefficient must be greater than 0.85
C.   The least squares regression line has a negative gradient
D.   The slope of the least squares regression line is 0.92
E.   Time spent watching television is the independent variable.

I said C. But answer is E.
?

By saying C is true, you are assuming that as the number of hours students spend watching television increases, the number of hours spent doing homework decreases. While this is the most likely scenario, you are not allowed to assume whether the gradient is positive or negative. Answer A, B, C, and D all assume that the gradient or slope is either positive or negative. From the given information, you cannot conclude definitively whether the gradient will be positive or negative, and therefore must select the answer that is 100% true, not merely probable.
Therefore, the answer is E.

Hope my explanation makes sense.

[ghadz7]

The 85% variation is r^2 = 0.85
r can be either negative or positive, and hence the gradient is either positive or negative. You have no further information to conclude whether the situation had a positive or negative relationship.

The variation is a dependant variable is explained by the variation of the independant variable. In that case, the hours they spent watching TV is independant.

[Studyinghard]

hm I understand now, I guess I shouldn't assume things.
IF ONLY more television meant getting more homework done eh ?

[onerealsmartass]

haha yeah i wish...

[TyErd]

yeah don't assume in these questions just refer back to the explanation: coefficient of determination tells us that ___% of the variation in the dependent variable can be explained by the variation in the independent variable.