Question

This Question: 1 pt 10 of 10 (7 complete) This Quiz: 10 pts possible A Question Help O Listed below are paired data consisting of movie budget amounts and the amounts that the movies grossed. Find the regression equation, letting the budget be the predictor (x) variable. Find the best predicted amount that a movie will gross if its budget is $125 million. Use a significance level of a = 0.05. Budget ($)in Millions 39 24 114 66 80 53 118 63 60 124 21 14 153 10 Gross ($) 121 20 95 66 in Millions 120 125 110 108 61 96 221 40 22 296 38 Click the icon to view the critical values of the Pearson correlation coefficient r. The regression equation is ý = 1 + x (Round to one decimal place as needed.) The best predicted gross for a movie with a $125 million budget is million. (Round to one decimal place as needed.)

Answer 1

The fitted regression equation for the given data is of the form $\widehat{Y}=\widehat{\beta_0}+\widehat{\beta_1}X$ . Where Y denotes the varible representing gross(in millions) and X denote the predictor variable budget in millions. $\widehat{\beta_0}$ is the Y intercept and $\widehat{\beta_1}$ is the slope. From linear regression analysis we get the following result(From Excel).

Calculations
b1, b0 Coefficients	1.3220	19.2241
b1, b0 Standard Error	0.2514	19.4407
R Square, Standard Error	0.6803	43.5822
F, Residual df	27.6608	13.0000

Where $\widehat{\beta_0}$ =19.2241$\approx$19.2

  $\widehat{\beta_1}$=1.3220$\approx$1.3

Therefore the fitted equation is $\widehat{Y}=19.2+1.3X$ ....................(1)

(b) Here we want to find the best predicted value of the gross for a movie with budget of $125. This can be obtained by substituting X=125 in  (1).

$\widehat{Y}=19.2+1.3X\Rightarrow \widehat{Y}=19.2+1.3\times 125=\$ 181.7\,million$