Question

1. a certain state law requires residential properties to receive an appraisal for tax purposes every six years. a random sample of 25 appraised properties was selected. the following scatterplot shows the value of the properties, in thousands of dollars, before and after the appraisal. also shown is the least-squares regression line and corresponding computer output. scatterplot and table omitted which of the following is not an appropriate description of the data in the sample? (a) new property values tend to be greater than old property values. (b) as old property values increase, new property values tend to increase. (c) the relationship between old and new property value is strong and positive. (d) for each additional $1,000 in old property value, the new property value increases by $955.97, on ave (e) the observed new property values typically deviate from the predicted new property values by about $

Explanation:

Step1: Analyze Option A

Check the regression line and scatterplot. The slope is less than 1 (0.95597), so for old values, new values: when old is \( x \), new is \( -3.817 + 0.95597x \). For \( x \) large, \( 0.95597x < x \) (since \( 0.95597 < 1 \)), so new values tend to be less than old? Wait, wait, no—wait, the y - axis is new, x - axis old. Wait, the constant is negative, slope ~0.956. Let's take an example: old = 200 (thousand), new = - 3.817+0.95597*200 = - 3.817 + 191.194 = 187.377, which is less than 200. So new values tend to be less than old? But option A says "New property values tend to be greater than old property values"—this seems incorrect. But let's check other options.

Step2: Analyze Option B

The slope of the regression line is positive (0.95597), so as old (x) increases, new (y) increases. So B is appropriate.

Step3: Analyze Option C

R - Sq is 98.28%, which is very high, and slope is positive, so the relationship is strong and positive. C is appropriate.

Step4: Analyze Option D

The slope of the regression line is 0.95597 (in thousands of dollars). So for each additional $1,000 (since x is in thousands) in old value, new value increases by 0.95597 thousand dollars, which is $955.97. So D is appropriate.

Step5: Analyze Option E (assuming E is about residual standard deviation)

\( S = 7.53867 \) (in thousands of dollars), so typical deviation from predicted is about $7,538.67, which matches "about $7,500" (if E says that). So E is appropriate.

So the inappropriate description is A.

Answer:

A. New property values tend to be greater than old property values.