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 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 $n = 74$ houses in East Meadow, the following result was obtained:
$$\hat { y } = 74.80 + 19.72 x$$
Which of the following statements concerning the deterministic model, $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ is true?

A) A plot of the predicted appraised values $y$ against the number of rooms $x$ for the sample of houses in East Meadow would not result in a straight line.
B) In theory, a plot of the mean appraised value $E ( y )$ against the number of rooms $x$ for the entire population of houses in east Meadow would result in a straight line.
C) In theory, if the appraised values $y$ and number of rooms $x$ for the entire population of houses in East Meadow were obtained and the $( x , y )$ data points plotted, the points would fall in a straight line.
D) All of the above statements are true.