Question

Movie Grosses. The data from Exercise$14.36$ on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site.

Short answer

(a) The model does not work well with the data. Furthermore, the residuals do not follow a normal distribution.

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that, Movie Grosses. The data from Exercise $14.36$ on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. We need to decide that whether we can reasonably apply the regression t-lest. If so, then also do part (b).

Part (a) Step 2: Explanation

DOMESTIC	OVERSEAS		$2$	$1.7$
$49$	$28.1$		$4.2$	$2.3$
$70$	$11.3$		$1.5$	$6$
$16$	$13.6$		$36.9$	$20.8$
$125$	$71.1$		$51.8$	$80.8$
$64.6$	$62.1$		$79.7$	$165.8$
$56$	$51.1$		$41.2$	$43.2$
$9$	$25.5$		$12.5$	$21.6$
$25.9$	$8.7$		$408$	$283.2$
$162.8$	$262.6$		$1.8$	$7.7$
$73.1$	$211.1$		$12.8$	$56.1$
$2.1$	$17.4$		$216.4$	$530.5$
$31.1$	$92$		$6$	$3.1$
$182.1$	$93.1$		$1.6$	$3.7$
$83.7$	$221.6$		$18.6$	$27.6$
$54.3$	$73.4$		$448.1$	$636.3$
$17.7$	$15.6$		$13.4$	$22.4$
$93.8$	$68$		$45.5$	$22.8$
$31.6$	$7.9$		$19.2$	$126.4$
$148.8$	$293$		$262$	490.2
$218.8$	$330.6$		$65.4$	$237.6$
$18.5$	$3.6$		$35.3$	$46.2$
$1$	$3.1$		$25.3$	$7.4$
$5.7$	$4$		$27.1$	103.4
$126.5$	$276,9$		$41.1$	$31$
$44.3$	$10.5$

MINITAB is used to create the residual plot.

Procedure with Minitab:

Step 1: Select Start >Regression$>$ Regression

Step 2: In the Response box, type OVERSEAS.

Step 3: In Predictors, select the DOMESTIC Column.

Step 4: In Graphs, under Residuals vs the variables, insert the columns DOMESTIC

Step 5: Click the OK button.

OUTPUT FROM MINITAB:

MINITAB is used to create a normal probability plot of residuals.

Part (a) Step 3: MINITAB output

OUTPUT FROM MINITAB:

The following is the assumption for regression inferences:

Line of population regression:

For each value $X$of the predictor variable, the conditional mean of the response variable $\left(Y\right)$is ${\beta }_0+{\beta }_{1}X$.

Standard deviation equal:

The response variable's $\left(Y\right)$standard deviation is the same as the explanatory variable's $\left(X\right)$standard deviation. The standard deviation is represented by the symbol $\sigma$.

Populations that are typical:

The response variable follows a normal distribution.

Observations made independently:

The response variable observations are unrelated to one another.

Examine whether the regression t-test is appropriate.

• The residual plot clearly shows that the residuals fall into a funnel form.
• It is obvious from the residuals normal probability plot that the residuals are in the mild linear range.