Question

U.S. Presidents. The Information Please Almanac provides data on the ages at the inauguration and death of the presidents of the United States. We give those data on the WeissStats site for those residents who are not still living at the time of this writing.

Short answer

a). $9.705$is the estimate's standard error.

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

c). The regression inference assumptions for the variables death and inauguration are not violated.

Step-by-step solution

Part (a) Step 1: Given Information

The Information Please Almanac provides data on the ages at the inauguration and death of the presidents of the United States.

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: Fill in the Death field in the Response column.

Step 3: Add the Inauguration column to Predictors.

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

MINITAB output:

Part (b) Step 1: Given Information

The Information Please Almanac provides data on the ages at the inauguration and death of the presidents of the United States.

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: Fill in the Death field in the Response column.

Step 3: Add the Inauguration column to Predictors.

Step 4: Under Residuals versus the variables, enter the columns Inauguration in Graphs.

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

Output MINITAB:

MINITAB is used to create a residuals normal probability graphic.

The procedure with MINITAB:

Select Stat >Regression >Regression as the first step.

Step 2: Fill in the Death field in the Response column.

Step 3: Add the Inauguration column to Predictors.

Select 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

The Information Please Almanac provides data on the ages at the inauguration and death of the presidents of the United States.

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 observations of the response variable are independent of one another.

Examine the graph for evidence of a violation of one or more of the regression inference assumptions.

- The residual plot clearly shows that the residuals lie within the horizontal band.

- The residuals are clearly linear based on the normal probability plot.

As a result, the regression inference assumptions for the variables death and inauguration are not violated.