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.

Box Office Mojo collects and posts data on movie grosses.

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:

Box Office Mojo collects and posts data on movie grosses.

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:

Box Office Mojo collects and posts data on movie grosses.

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.