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

Title First_Weekend National_Gross Wordwide_Gross Movie_A 90.954 317.772 976.513 Movie_B 88.678 261.204 878.526 Movie_C 93.557 249.323 795.982 Movie_D 102.404 290.506 896.861 Movie_E 77.283 292.021 938.303 Movie_F 77.963 301.375 934.788

Explanation / Answer

a) covariance between first weekend gross and national gross, = -55.783

Sum(X) =90.954 + 88.678 + 93.557 + 102.404 + 77.283 + 77.963 = 530.839
XMean = 88.473
Sum(Y) =317.772 + 261.204 + 249.323 + 290.506 + 292.021 + 301.375 = 1712.2009999999998
YMean = 285.367
Covariance(X,Y) = SUM(xi - xmean)*(yi - ymean)/(samplesize -1)
= (90.954-88.473)*(317.772-285.367)+(88.678-88.473)*(261.204-285.367)+(93.557-88.473)*(249.323-285.367)+(102.404-88.473)*(290.506-285.367)+(77.283-88.473)*(292.021-285.367)+(77.963-88.473)*(301.375-285.367))/5
= -55.783

b) Compute the covariance between , first weekend gross and worldwide gross = -236.273

Sum(X) =90.954 + 88.678 + 93.557 + 102.404 + 77.283 + 77.963 = 530.839
XMean = 88.473
Sum(Y) =976.513 + 878.526 + 795.982 + 896.861 + 938.303 + 934.788 = 5420.973
YMean = 903.496
Covariance(X,Y) = SUM(xi - xmean)*(yi - ymean)/(samplesize -1)
= (90.954-88.473)*(976.513-903.496)+(88.678-88.473)*(878.526-903.496)+(93.557-88.473)*(795.982-903.496)+(102.404-88.473)*(896.861-903.496)+(77.283-88.473)*(938.303-903.496)+(77.963-88.473)*(934.788-903.496))/5
= -236.273

c) the covariance between national gross and worldwide gross. =  1508.626

Sum(X) =317.772 + 261.204 + 249.323 + 290.506 + 292.021 + 301.375 = 1712.2009999999998
XMean = 285.367
Sum(Y) =976.513 + 878.526 + 795.982 + 896.861 + 938.303 + 934.788 = 5420.973
YMean = 903.496
Covariance(X,Y) = SUM(xi - xmean)*(yi - ymean)/(samplesize -1)
= (317.772-285.367)*(976.513-903.496)+(261.204-285.367)*(878.526-903.496)+(249.323-285.367)*(795.982-903.496)+(290.506-285.367)*(896.861-903.496)+(292.021-285.367)*(938.303-903.496)+(301.375-285.367)*(934.788-903.496))/5
= 1508.626

No.of Inputs 6 X Mean 88.473 Y Mean 285.367 Covariance(X,Y) -55.783 Calculation

Sum(X) =90.954 + 88.678 + 93.557 + 102.404 + 77.283 + 77.963 = 530.839
XMean = 88.473
Sum(Y) =317.772 + 261.204 + 249.323 + 290.506 + 292.021 + 301.375 = 1712.2009999999998
YMean = 285.367
Covariance(X,Y) = SUM(xi - xmean)*(yi - ymean)/(samplesize -1)
= (90.954-88.473)*(317.772-285.367)+(88.678-88.473)*(261.204-285.367)+(93.557-88.473)*(249.323-285.367)+(102.404-88.473)*(290.506-285.367)+(77.283-88.473)*(292.021-285.367)+(77.963-88.473)*(301.375-285.367))/5
= -55.783

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