Question

Acreage and Value. The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. On the WeissStats site are data on lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area.

Short answer

a). $139.012$ is the estimate's standard error.

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

c). The variable's value and lot size do not violate the assumptions for regression inferences.

Step-by-step solution

Part (a) Step 1: Given Information

On the WeissStats site are data on lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area.

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 out the Value column in the Response section.

Step 3: Add the columns Lot Size to Predictors.

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

Part (b) Step 1: Given Information

On the WeissStats site are data on lot size (in acres) and assessed value (in thousands of dollars) for a sample of homes in a particular area.

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 out the Value column in the Response section.

Step 3: Add the columns Lot Size to Predictors.

Step 4: Under Residuals vs the variables, enter the columns Lot Size.

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

Output:

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 out the Value column in the Response section.

Step 3: Add the columns Lot Size 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

Regression inferences 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 to see if one or more of the regression inference assumptions are violated.

- The horizontal band of residuals is clearly visible on the residual plot.

- The residuals have a nearly linear trend, as evidenced by the normal probability plot of residuals.

As a result, the variables value and lot size do not violate the assumptions for regression inferences.