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:

Unaided Recall Test

A measure of memory in which respondents are asked to remember specific information without the use of any prompts or cues, often used in market research to assess brand awareness.

Jury Test

A method used in marketing research where a product, ad, or campaign is evaluated by a panel of judges or potential consumers for feedback.

Aided Recall

A market research technique where respondents are prompted with specific cues or aids to help them remember certain information or brands.

Starch Test

A chemical method used to detect the presence of starch in a substance, typically involving iodine solution, which turns blue-black in the presence of starch.