Question

Movie Grosses. Box Office Mojo collects and posts data on movie grosses. For a random sample of $50$ movies, we obtained both the domestic (U.S.) and overseas grosses, in millions of dollars. The data are presented on the WeissStats site.

Short answer

a). $77.8401$is the estimate's standard error.

b). The residual and normal probability plots are produced.

c). For the variables overseas and domestic, the regression inference violates assumptions $1$and $3$.

Step-by-step solution

Part (a) Step 1: Given Information

Box Office Mojo collects and posts data on movie grosses.

Part (a) Step 2: Explanation

MINITAB can be used to calculate the standard error of an estimate.

The procedure with MINITAB:

Select Stat >Regression >Regression as the first step.

Step 2: Select OVERSEAS from the Response column.

Step 3: Add the columns DOMESTIC to Predictors.

Step 4: Select OK from the drop-down menu.

output MINITAB:

Part (b) Step 1: Given Information

Box Office Mojo collects and posts data on movie grosses.

Part (b) Step 2: Explanation

Using MINITAB, create a residual plot.

The procedure with MINITAB:

Select Stat >Regression >Regression as the first step.

Step 2: Select OVERSEAS from the Response column.

Step 3: Add the columns DOMESTIC to Predictors.

Step 4: Under Residuals vs the variables in Graphs, insert the columns DOMESTIC.

Step 5: Select OK from the drop-down menu.

MINITAB is used to create a residuals normal probability graphic.

The procedure with MINITAB:

Select Stat >Regression >Regression as the first step.

Step 2: Select OVERSEAS from the Response column.

Step 3: Add the columns DOMESTIC to Predictors.

Select the Normal probability plot of residuals from the Graphs menu.

Step 5: Select OK from the drop-down menu.

output MINITAB:

Part (c) Step 1: Given Information

Box Office Mojo collects and posts data on movie grosses.

Part (c) Step 2: Explanation

Regression conclusions are based on the following assumptions:

Regression line of the population:

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

The standard deviation is the same for both groups:

The response variable's standard deviation is the same as the explanatory variable's standard deviation. $\sigma$is the symbol for standard deviation.

Populations in the normal range:

The response variable has a normally distributed distribution.

The response variable's observations are independent of one another.

Examine the graph for any indications of a violation of one or more of the regression inferences assumptions.

- The funnel form of the residuals can be seen on the residual plot.

- The residuals are in a mild linear pattern, as shown by the normal probability plot of residuals.

As a result, for the variables overseas and domestic, assumptions $1$ and $3$for regression inferences are violated. In other words, the model does not work well with the data. Furthermore, the residuals are not distributed regularly.