I am taking an introductory level statistics class, and I need help interpreting the equation of the regression line, which is:
Predicted audience rating =-33 + 0.482 critics rating
According to the regression line, is it true that, on average, audiences tend to rate movies higher than critics do?
a)no, because the slope is less than one
b)no because the slope is less than one and the intercept is no 0
c)yes because the slope is positive
d) yes because the slope is positive and the intercept is positive.
I know for sure that the answer cannot be D. I plugged in values for critics rating to get the predicted audience rating to see the relationship, and I found that the critic's ratings were always lower than the audience's (I plugged in positive values). So my guess is that the answer is C.
Am I correct on this? If I could get help on this problem, I would greatly appreciate it. Thanks.
None of the proposed answers is satisfactory, this is a poorly formulated question.
Actually, audiences rate lower because the slope is less than one and the intercept is negative. Both conditions are required to be affirmative, as we don't know the distribution of the ratings.
a) with a slope less than one and a positive intercept, the average could still be higher;
b) with a slope less than one and a positive intercept, the average could still be higher;
c) also inconclusive;
d) wrong.
If the average of the critics ratings is known, let $r$, and provided the range doesn't cause impossible rating values (such as negative), the average audience rating is
$$0.482r-33$$ which you can compare to $r$.
With these coefficients, you certainly have
$$0.482r-33<r.$$