The following table presents statistics, specically correlation coecients, from

Question

The following table presents statistics, specically correlation coecients, from a data set with 4 variables on the revenues and popularities of 100 movies. Opening Gross is the money made in the rst weekend it was in theaters; Total Gross is total money made; Number of Theaters is the number of theaters it played in; and Weeks in Top 60 is the number of weeks it was in the top 60 most watched movies. For each variable pair in (a)-(f), interpret what the correlation coecient is telling you about the relationship between those variables. Then, answer the questions in (g)-(j).

Correlations in the Movie Business
Variable pair                                              Correlation coecient
Opening Gross & Total Gross                      0.964
Opening Gross & Number of Theaters    0.714
Opening Gross & Weeks in Top 60 0.453
Total Gross & Number of Theaters 0.710
Total Gross & Weeks in Top 60    0.525
Number of Theaters & Weeks in Top 60    0.526

(a) Opening Gross & Total Gross
(b) Opening Gross & Number of Theaters
(c) Opening Gross & Weeks in Top 60
(d) Total Gross & Number of Theaters
(e) Total Gross & Weeks in Top 60
(f) Number of Theaters & Weeks in Top 60
(g) What is the strongest relationship reported?
(h) What is the weakest relationship reported?
(i) If a movie makes a lot of money in its opening weekend, would we say we expect it to
stay in the top 60 for a long time?
(j) If a movie makes a lot of money in its opening weekend, would we say we expect it to
make a lot of money overall?

Explanation / Answer

g) Strongest relationship is Opening Gross & Total Gross since it has the highest correlation coefficient (0.964) amongst all h) Weakest relationship is Opening Gross & Weeks in Top 60 since it has the lowest correlation coefficient (0.453) amongst all i) We will NOT say that the if a movie makes a lot of money in its opening weekend, we expect it would stay in the top 60 for a long time since the correlation coefficient between Opening Gross & Weeks in Top 60 is 0.453 which is not very high in fact the lowest. j) We will CERTAINLY say that if a movie makes a lot of money in its opening weekend, we expect it to make a lot of money overall since the correlation coefficient between Opening Gross & Total Gross = 0.964 which is very high

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