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

​$125

million. Use a significance level of

alpha equals 0.05α=0.05.

Budget left parenthesis $ right parenthesisBudget ($)in Millionsin Millions	3939	2121	114114	6969	7575	5454	115115	6868	99	6565	126126	1616	1111	148148	88
Gross left parenthesis $ right parenthesisGross ($) in Millionsin Millions	123123	1616	104104	7474	123123	108108	9494	107107	4747	105105	205205	3434	1212	293293	4040

Answer 1

Here, x = Budget (in Millions), y = Gross (in Millions).
The values are: x = (39, 21, 114, 69, 75, 54, 115, 68, 9, 65, 126, 16, 11, 14), y = (123, 16, 104, 74, 123, 108, 94,107, 47, 105, 205, 34, 12, 29). We input this data set in R programming software and use the summary(.) and lm(.) functions to answer the given question. The R code and output is given below.

> x = c(39, 21, 114, 69, 75, 54, 115, 68, 9, 65, 126, 16, 11, 14)
> y = c(123, 16, 104, 74, 123, 108, 94,107, 47, 105, 205, 34, 12, 29)
> mb=lm(y~x)
> summary(lm(y~x))

Call:
lm(formula = y ~ x)

Residuals:
Min 1Q Median 3Q Max
-50.233 -24.565 1.443 18.034 57.032

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25.8053 15.8375 1.629 0.129184
x 1.0298 0.2292 4.494 0.000735 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 33.69 on 12 degrees of freedom
Multiple R-squared: 0.6272, Adjusted R-squared: 0.5962
F-statistic: 20.19 on 1 and 12 DF, p-value: 0.0007347

The regression equation is given as: = 25.8053 + (1.0298) (Please round the coefficients to the required number of decimal places).
Now, for = 125, predicted value of Gross = 25.8053 + (1.0298 * 125) = 154.53 millions (Please round the coefficients to the required number of decimal places).