A company that holds the DVD distribution rights to movies previously released o

Question

A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in Smillions) for each of 22 movies in the year that they were released and the DVD revenue (in Smilions) in the following year are shown in the accompanying table, along with the summary statistics. A linear regression was performed on this data, and the result is the linear regression equation Y 10.762+0.3844X. Complete parts (a) through (d) below. Click on the icon to view the data table. a. Determine the coefficient of determination, , and interpret its meaning r2 = (Round to four decimal places as needed.)

Explanation / Answer

a. Here as per formula

r2 =  [nxy - xy]2 / [n(x2 - (x)2] [n(y)2 - y2]

r2 = [ 22 * 84391.9153 - 1711.27 * 894.60]2 / [22 * 171625.5227 - 1711.272] * [22 * 47084.6128 - 894.602]

r2 = 106093514882.224/ (847316.4865 * 235552.3216) = 0.5316

here we can interpret R - square as the percentage of variation in independnet variable (y) explained by dependent variable (x).

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