A County Real Estate Appraiser Wants to Develop a Statistical $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$

Multiple Choice

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be
An important predictor of appraised value is the number of rooms in the house. Consequently, the
Appraiser decided to fit the simple linear regression model: $$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$$
where $\mathrm { y } =$ appraised value of the house (in thousands of dollars) and $x =$ number of rooms. Using data collected for a sample of $n = 74$ houses in East Meadow, the following results were obtained:
$$\hat { y } = 74.80 + 19.72 x \quad R = 0.539 \quad R ^ { 2 } = 0.290 \quad s = 58.031$$
Give a practical interpretation of the estimate of $\sigma$ , the standard deviation of the random error term in the model.

A) We expect to predict the appraised value of an East Meadow house to within about $\$ 29,000$ of its true value.
B) We expect $95 \%$ of the observed appraised values to lie on the least squares line.
C) We expect to predict the appraised value of an East Meadow house to within about $\$ 58,000$ of its true value.
D) About $29 \%$ of the total variation in the sample of $y$ -values can be explained by the linear relationship between appraised value and number of rooms.