5.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 90.715 317.244 976.489

Movie B 88.316 261.708 878.994

Movie C 93.962 249.131 795.479

Movie D 102.921 290.569 896.828

Movie E 77.207 292.711 938.495

Movie F 77.873 301.041 934.477

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