Question

The data from Exercise 14.43 for volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines are on the WeissStats site.

Short answer

(a) For the variables volume and diameter, the regression inferences assumption is broken.

Step-by-step solution

Part (a) Step 1: Given information

Given in the question that, The data from Exercise 14.43 for volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines 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

Given:

MINITAB is used to create the residual plot.

Minitab Procedure:

To begin, select Start > Regression > Regression.

Step 2: In the Response field, type VOLUME.

Step 3: Select Column DIAMETER in Predictors.

Step 4: In Graphs, under Residuals vs the variables, enter the columns DIAMETER.

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 procedure

Procedure with Minitab:

To begin, select Start > Regression > Regression.

Step 2: In the Response field, type VOLUME.

Step 3: Select Column DIAMETER in Predictors.

Step 4: Select Normal probability plot of residuals from the Graphs menu.

Step 5: Click the OK button.

OUTPUT FROM MINITAB:

The following is the assumption for regression inferences:

Line of population regression:

For each value of the predictor variable $X$, 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.

Independent Observations: The responses variable observations are unrelated to one another.

Examine whether the regression t-test is appropriate to use.

• It is obvious from the residual plot that the residuals follow a curved concave rising pattern.
• It is clear from the normal probability plot of residuals and the residual plot that there are outliers in the data. As a result, the residual plot has greater fluctuation than the standard probability map for residuals.