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Movie companies need to predict the gross receipts of individual movies after a movie has debuted....

Question

Movie companies need to predict the gross receipts of individual movies after a movie has debuted....

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..

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

QUESTION 1: Find the covariance between first weekend gross and national gross. nothing ​(Round to four decimal places as​ needed.)

Title First Weekend   National Gross   Wordwide Gross
Movie A 90.868 317.036 976.867
Movie B 88.947 261.469 878.796
Movie C 93.682 249.394 795.296
Movie D 102.506 290.303 896.347
Movie E 77.133 292.853 938.099
Movie F 77.965 301.232 934.742

Math Statistics And Probability
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Answers

We will calculate the sample covariances, as the data we have is a sample of 6 movies.

Sample covariance between 2 variables X and Y is calculated as (we will use n-1 as the denominator, as against "n" in case of population covariance)

Cov(X,Y)=rac{1}{n-1}sum(x-ar{x})(y-ar{y})

where n is the number of observations

ar{x}=rac{sum x}{n} is the sample mean of X

ar{y}=rac{sum y}{n} is the sample mean of Y

Let X be the First Weekend gross

Y be the National gross

Z be the worldwide gross

The sample means are

90.868 +88.947+93.682 102.50677.133 +77.965 88.517 6
Σ yー317.0364 26 1.4694 249391+ 290.303 + 292.853 + 301.232-285.381 6

Σ ~ 976.867 + 878.796 + 795.296 + 896.347 + 938.099 + 934.742 6 2 903.358

a) the sample covariance between first weekend gross (X) and national​ gross (Y) is

((90.868-88.517) × (317.036-285.281) + (88.947-88.517) × (26 1.469-285.281) (93.682-88.517) × (249.394-285.281) (102.506-88.517) × (290.303-285281) (77.133-88.517) × (292.853-285.281) + (77.965-88.517) × (30 1.232-285.281)) =-61.0403

ans: The sample covariance between first weekend gross and national​ gross is -61.0403

the sample covariance between first weekend gross (X) and worldwide​ gross (Z) is

Cor(X, Z) = ((90.868-88.517) × (976.867-903.358) + (88.947-88.517) × (878.796-903.358) + (93.682-88.517) × (795.296-903.358) + (102.506-88.517) × (896.347-903.358) + (77.133-88.517〉、(938.099-903.358) + (77.965-88.517) × (934.742-903.358)) -244.1229

ans: the sample covariance between first weekend gross and worldwide​ gross is -244.1229

The sample covariance between national gross (Y) and worldwide gross (Z) is

Cor (Y, Z) = 317.036- 285.381) (976.867 903.358) +。 26 1.469-285381) × (878.796-903.358 249.394-285.381) × (795.296-903.358) + (290.303-285.381) × 896.347-903.358) + (292.853-285.381) × (938. 285.381) x 099-903.358)+(301 .232 285.381) × (934.742-903.358) ) - 6-1 1505, 1251

ans: The sample covariance between national gross and worldwide gross is 1505.1251

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