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

Short Answer

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 $y =$ appraised value of the house (in thousands of dollars) and $x =$ number of rooms. Using data collected for a sample of $n = 80$ houses in East Meadow, the following results were obtained:
$$\hat { y } = 80.80 + 19.72 x$$
What are the properties of the least squares line, $\hat { y } = 80.80 + 19.72 x ?$
A) Average error of prediction is 0 , and $S S E$ is minimum.
B) It is normal, mean 0 , constant variance, and independent.
C) All 80 of the sample $y$ -values fall on the line.
D) It will always be a statistically useful predictor of $y$ .