Question

the following table shows the appraised value of a house over time. age (years) value (thousands) 0 140 3 148 6 160 9 162 12 185 15 178 18 194 using the data from the table determine if there is a linear trend between the age of a house and its value and determine there is an exact linear fit of the data. describe the linear trend if there is one. a. negative linear trend, an exact linear fit. b. negative linear trend, not an exact linear fit. c. positive linear trend, an exact linear fit. d. positive linear trend, not an exact linear fit.

Explanation:

Step1: Observe age - value relationship

As age increases from 0 to 18 years, value generally increases (from 140 to 194 in thousands), so positive trend.

Step2: Check for exact linearity

If it were exact linear, the rate of change of value with respect to age would be constant. But $\frac{148 - 140}{3-0}=\frac{8}{3}$, $\frac{160 - 148}{6 - 3}=4$, rates are not equal, so not exact linear fit.

Answer:

d. Positive linear trend, not an exact linear fit.