Stats 110A, Fall '99 Quiz 3 Oct. 29, 1999
NAME:
A study collected some data on all Broadway shows playing in New York City during a particular time period. We'll examine just two variables. "Capacity" is the total number of seats in the theater in which the play/musical was playing. "Receipts" is the dollars that theater collected for that play/musical during the time period. (The shows themselves are at the end of the quiz.)
The correlation, r, is 0.821
And now the questions...(Turn page)
1. (2) How are receipts are related to the capacity of the theater?
Bigger theaters tend to have higher receipts, which makes sense since theaters make money for each seat they sell. This trend looks roughly linear, but is not terribly strong.
2. (4) Find the regression line.
b = (s_y/ s_x) * r = (187724/2664.09)*.821 = 55.1087
a = ybar - b*xbar (which you can derive from the equation of a line, once you know that the regression line must pass through the point (xbar,ybar) = 345533 - 55.1087*9997.33 = -205406.860
yhat = -205406.860 + 55.1087x
3. (4) Interpret the regression line.
The intercept is not really interpretable since we examined no 0-seat theaters. However, the slope suggests that theaters with one additional seat make, on average, $55 more than theaters without that additional seat. This might be a good estimate for the average cost of a seat for this collection of shows (although it seems a little low).
Angels in America, Blood Brothers , Cats , Crazy for You, Falsettos,
Fool Moon, The Goodbye Girl , Guys and Dolls, Jelly's Last Jam, Kiss of the Spider Woman, Les Miserables , Miss Saigon , Phantom of the Opera , Shakespeare for My Father, The Sisters Rosenswieg, Someone Who'll Watch over Me,
Tommy, The Will Rogers Follies