Movie companies need to predict the gross receipts of individual movies after a movie has debuted. The accompanying results are the first-weekend gross, the national gross, and the worldwide gross (in millions of dollars) of six movies. Complete parts (a) through (d) below.

Gross receipts of six movies

Title First Weekend National Gross Worldwide Gross

Movie A 90.028 317.807 976.292

Movie B 88.388 261.552 878.783

Movie C 93.609 249.584 795.062

Movie D 102.708 290.927 896.228

Movie E 77.444 292.322 938.145

Movie F 77.662 301.718 934.113

a. Compute the covariance between first-weekend gross and national gross, first weekend gross and worldwide gross, and national gross and worldwide gross.

Compute the covariance between first weekend gross and national gross.

cov(X,Y)= _____________ (Round to four decimal places as needed.)

Compute the covariance between the first-weekend gross and worldwide gross.

cov(X,Y)=_________ (Round to four decimal places as needed.)

Compute the covariance between national gross and worldwide gross.

cov(X,Y)=_________ (Round to four decimal places as needed.)

b. Compute the coefficient of correlation between first-weekend gross and national gross, first-weekend gross and worldwide gross, and national gross and worldwide gross.

Compute the coefficient of correlation between first-weekend gross and national gross.

R= ___________(Round to four decimal places as needed.)

Compute the coefficient of correlation between first-weekend gross and worldwide gross.

R= ___________(Round to four decimal places as needed.)

Compute the coefficient of correlation between national gross and worldwide gross.

R= ___________(Round to four decimal places as needed.)

c. Which is more valuable in expressing the relationship between first-weekend gross, national gross, and worldwide gross, the covariance or the coefficient of correlation? Explain.

A. The correlation coefficient is more valuable for expressing the relationship between first weekend gross, national gross, and worldwide gross because it does not depend on the units used to measure first weekend gross, national gross, and worldwide gross.

B. The covariance is more valuable for expressing the relationship between first weekend gross, national gross, and worldwide gross because it measures the relative strength between first weekend gross, national gross, and worldwide gross.

C. The correlation coefficient is more valuable for expressing the relationship between first weekend gross, national gross, and worldwide gross because it can prove that there is a causation effect between first weekend gross, national gross, and worldwide gross.

d. Based on (a) and (b), what conclusions can be reached about the relationship between first weekend gross, national gross, and worldwide gross?

A. There is a weak negative linear relationship between first-weekend gross and both national gross and worldwide gross. There is a strong positive linear relationship between national gross and worldwide gross.

B. There is a strong negative linear relationship between first-weekend gross and both national gross and worldwide gross. There is a strong positive linear relationship between national gross and worldwide gross.

C. There is a weak positive linear relationship between the first-weekend gross and both national gross and worldwide gross. There is a strong negative linear relationship between national gross and worldwide gross.