PCBs and Pelicans. Use the data points given on the WeissStats site for shell thickness and concentration of PCBs for 60 Anacapa pelican eggs referred to in Exercise 14.40.

Given in the question that, PCBs and Pelicans. Use the data points given on the WeissStats site for shell thickness and concentration of PCBs for 60 Anacapa pelican eggs referred to in Exercise 14.40.
We need to decide that whether we can reasonably apply the regression t-lest. If so, then also do part (b).

Given:

MINITAB is used to create the residual plot.

Procedure with Minitab:

To begin, select Start > Regression > Regression.

Step 2: Fill in the THICKNESS column in the Response.

Step 3: Select Column PCB in Predictors.

Step 4: In Graphs, under Residuals versus the variables, enter the columns PCB.

Step 5: Click the OK button.

Construct the normal probability plot of residuals by using MINITAB

Step 1: Select Start > Regression > from the Minitab menu. Regression

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

Step 3: Select Column PCB from Predictors.

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

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

output MINITAB:

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 for the response variable $\left(Y\right)$and the standard deviation for the explanatory variable $\left(X\right)$are the same. 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.

• It's evident from the residual plot that the residuals are in the horizontal band.
• It is obvious from the normal probability plot of residuals that the residuals follow a linear trend.