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The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x1), in thousands of dollars, and newspaper advertising (x2), in thousands of dollars. The estimated regression equation was ŷ = 83.2 + 2.29x1 + 1.30x2.


(a) What is the gross revenue (in dollars) expected for a week when $4,000 is spent on television advertising (x1 = 4) and $1,500 is spent on newspaper advertising (x2 = 1.5)? (Round your answer to the nearest dollar.)

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Answer:

Y = 83.2 + 2.29x1  + 1.30x2

Y = 83.2 + 2.29(4) + 1.30(1.5)

Y = 83.2 + 9.16 + 1.95

Y = 94.31(thousand)

Y = $94,310

The gross revenue is $94,310

Explanation:

In this case, the estimated regression equation has been given.  Since x1 is $4,000 and x2 is $1,500, then, we will substitute these values for x1  and x2 in the equation. The addition of all values after the substitution gives the gross revenue.