91Ó°ÊÓ

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).

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.

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 ${\mathrm{β}}_0+{\mathrm{β}}_{1}X$.

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 $\mathrm{σ}$.

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.