In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts $\left(b\right)-\left(h\right)$.
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a $95\%$ confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a $95\%$ prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).

14.101 Acreage and Value. The data from Exercise $14.37$for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site. Specified value of the predictor variable: $2.5$ acres.

To decide whether reasonably apply the conditional mean and predicted value$t$-interval procedures to the data.

The data from Exercise $14.37$for lot size (in acres) and assessed value is as follows:

Using the data from Exercise 14.37, determine if it is reasonable to apply the conditional mean and predated value t-interval technique to data.
It is obvious from the residual plot that the residuals fall into the horizontal band.
It is obvious from the normal probability plot of residuals that the residuals follow a fairly linear trend.
Therefore, the variables value and lot size do not violate assumptions $1-3$ for regression inferences.
However, it is obvious from Exercise$14.73$ that the observations do not follow a linear trend.
As a result, applying the conditional mean and predicted value $t$-interval technique to the data is not reasonable.
As a result, portions (b) through (f) are eliminated.

To determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

For provided data, it is not reasonable to use the conditional mean and predicted value $t$-interval technique.
As a result, sections (b) - (f) are eliminated.

To find and interpret a $95\%$ confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.

For provided data, it is not reasonable to use the conditional mean and predicted value $t$-interval technique.
As a result, sections (b) - (f) are eliminated.

To determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.

For provided data, it is not reasonable to use the conditional mean and predicted value $t$-interval technique.
As a result, sections (b) - (f) are eliminated.

To find and interpret a $95\%$prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.

For provided data, it is not reasonable to use the conditional mean and predicted value$t$-interval technique.
As a result, sections (b) - (f) are eliminated.

To compare and discuss the differences between the confidence interval that obtained in part (c) and the prediction interval that obtained in part (e).

For provided data, it is not reasonable to use the conditional mean and predicted value $t$-interval technique.
As a result, sections (b) - (f) are eliminated.