Question

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 $105 million. Use a significance level of a 0.05 Budget (S)in Millions Gross (S) in Millions 41 18 111 70 70 57 121 68 11 64 122 17 13 147 50 113 18 105 64 114 116 103 96 48 94 213 41 19 298 46 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is y 16.01.3x (Round to one decimal place as needed.) The best predicted gross for a movie with a $105 million budget is S (Round to one decimal place as needed.) million

Answer 1

The statistical software output for this problem is:

Simple linear regression results: Dependent Variable: Gross Independent Variable: Budget Gross 16.0230311.3343899 Budget Sample size: 15 R (Correlation coefficient) 0.83015642 R-sq 0.68915969 Estimate of error standard deviation: 42.727584 Parameter estimates: Std. Err Alternative DF P-value Parameter Estimate T-Stat 0 13 0.84244517 0.4148 Intercept 16.023031| 19.019672 Slope 1.3343899 0.24855345 0 13 5.3686234 0.0001 Analysis of variance table for regression model: P-value Source DF SS MS F-stat Model 1 52618.996 52618.996 28.822117 0.0001 Error 13 23733.404 1825.6465 Total 14 76352.4 Predicted values: s.e. ( Pred. y) X value Pred. Y 95% C.I. for mean 95% P.I. for new 15.302767 (123.07435, 189.19359) (58.085091, 254.18284) 105 156.13397

Hence,

Regression equation:

$\small \widehat{y}$ = 16.0 + 1.3 x

Best predicted gross = $ 156.1 million