Please answer all sections Dixie Showtime Movie Theaters, Inc., owns and operate
ID: 2946078 • Letter: P
Question
Please answer all sections
Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. Television Advertising ($100s) Newspaper Advertising ($100s) Weekly Gross Market Revenue ($%100s) 103.5 Mobile Shreveport Jackson Birmingham Little Rock Biloxi New Orleans Baton Rouge 51.6 75.8 127.8 134.8 101.4 237.8 219.6 4.9 3.3 4 4.2 3.2 3.6 5 6.7 1.7 3 1.5 4 4.3 2.2 8.5 5.9 (a) Use the data to develop an estimated regression with the amount of television advertising as the independent variable. Let x represent the amount of television advertising. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)Explanation / Answer
(a) On regressing weekly gross revenue (y) on Television advertising (x1) by least square method we get the following regression equation,
Y = -46.82 +40.89 * x1 ; Y is the predicted value of y
(b) From the fitted model we find the percentage of total variation of y explained by this model is
(explained sum of squares )/(Total sum of squares) = 51.81 %
(c) On regressing y on x1 and x2 by least square method we get the following regression equation
Y = -40.27 + 21.66 * x1 + 19.89 *x2
(d )From the fitted model we find the percentage of total variation of y explained by this model is
( ESS) / (TSS) = 92.14 %
Thus, we see as we include x2 in the model suddenly the explained total variation of y has increased from
51.81 % to 92.14 %