Interpret the Slope and the Y-Intercept of the Least-Squares Regression $x$

question 5

Multiple Choice

Interpret the Slope and the y-intercept of the Least-Squares Regression Line
-A real estate magazine reported the results of a regression analysis designed to predict the price (y) , measured in dollars, of residential properties recently sold in a northern Virginia subdivision. One independent variable used to predict sale price is GLA, gross living area ( $x$ ) , measured in square feet. Data for 157 properties were used to fit the model, $\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }$ . The results of the simple linear regression are provided below.
$$\hat { \mathrm { y } } = 96,600 + 22.5 \mathrm { x } \quad \mathrm { s } = 6500 \quad \mathrm { r } ^ { 2 } = - 0.77 \quad \mathrm { t } = 6.1 \text { (for testing } \beta _ { 1 } \text { ) }$$
Interpret the estimate of $\beta 0$ , the $y$ -intercept of the line.

• A) There is no practical interpretation, since a gross living area of 0 is a nonsensical value.
• B) All residential properties in Virginia will sell for at least \(\$ 96,600\).
• C) About \(95 \%\) of the observed sale prices fall within \(\$ 96,600\) of the least squares line.
• D) For every 1-sq ft. increase in GLA, we expect a property's sale price to increase \(\$ 96,600\).

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Definitions:

Cash Equivalents

Short-term, highly liquid investments that are easily convertible to known amounts of cash, typically with original maturities of three months or less.