Movie companies need to predict the gross receipts of individual movies after a

Question

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. Click the icon to view the gross receipts of the six movies 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(XY)- (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. Gross receipts of six movies | | (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. rRound to four decimal places as needed.) Click to select your answer(s). First National Worldwide Weekend Gross Gross Title Mov vie A90.044 317.339 976.152 88.867 261.453 878.362 C 93.221 249.126 795.194 Movie D 02.027 290.417 896.603 Movie E 77.397 292.507 938.083 Movie F77.803 301.897 934.593 Movie B Movie

Explanation / Answer

PART A.

covariance between first weekend and the national gross

calculation procedure for correlation
sum of (x) = x = 529.359
sum of (y) = y = 1712.739
sum of (x^2)= x^2 = 47148.5316
sum of (y^2)= y^2 = 492169.6536
sum of (x*y)= x*y = 150790.8233
to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)
covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1
= 150790.8233 - [ 6 * (529.359/6) * (1712.739/6) ]/6- 1
= -53.024

ii. covariance between first weekend and the world gross

calculation procedure for correlation
sum of (x) = x = 529.359
sum of (y) = y = 5418.987
sum of (x^2)= x^2 = 47148.5316
sum of (y^2)= y^2 = 4914086.7579
sum of (x*y)= x*y = 476879.4698
to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)
covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1
= 476879.4698 - [ 6 * (529.359/6) * (5418.987/6) ]/6- 1
= -203.1311

iii. covariance between national and the world gross

calculation procedure for correlation
sum of (x) = x = 1712.739
sum of (y) = y = 5418.987
sum of (x^2)= x^2 = 492169.6536
sum of (y^2)= y^2 = 4914086.7579
sum of (x*y)= x*y = 1554460.4004
to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)
covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1
= 1554460.4004 - [ 6 * (1712.739/6) * (5418.987/6) ]/6- 1
= 1262.5563

PART B.

i.regression b/w first week and the national gross

to calculate r( x,y) = -53.024/ (SQRT(1/6*150790.823342-(1/6*529.359)^2) ) * ( SQRT(1/6*150790.823342-(1/6*1712.739)^2)
=-53.024 / (8.6124*23.2994)
=-0.2642
value of correlation is =-0.2642

ii. regression b/w first week and the world gross

to calculate r( x,y) = -53.024/ (SQRT(1/6*150790.823342-(1/6*529.359)^2) ) * ( SQRT(1/6*150790.823342-(1/6*1712.739)^2)
=-53.024 / (8.6124*23.2994)
=-0.2642
value of correlation is =-0.2642

iii. regression b/w national and the world gross

to calculate r( x,y) = 1262.5563/ (SQRT(1/6*1554460.400411-(1/6*1712.739)^2) ) * ( SQRT(1/6*1554460.400411-(1/6*5418.987)^2)
=1262.5563 / (23.2994*57.5182)
=0.9421
value of correlation is =0.9421

( X) ( Y) X^2 Y^2 X*Y 90.044 317.339 8107.921936 100704.04 28574.47292 88.867 261.453 7897.343689 68357.671 23234.54375 93.221 249.126 8690.154841 62063.764 23223.77485 102.03 290.417 10409.50873 84342.034 29630.37526 77.397 292.507 5990.295609 85560.345 22639.16428 77.803 301.897 6053.306809 91141.799 23488.49229

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