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Interpret the Slope and the Y-Intercept of the Least-Squares Regression xx

Question 99

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 ( xx ) , measured in square feet. Data for 157 properties were used to fit the model, y=β0+β1x\mathrm { y } = \beta _ { 0 } + \beta _ { 1 } \mathrm { x } . The results of the simple linear regression are provided below.
y^=96,600+22.5xs=6500r2=0.77t=6.1 (for testing β1 )  \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 β0\beta 0 , the yy -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\$ 96,600 .
C) About 95%95 \% of the observed sale prices fall within $96,600\$ 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\$ 96,600 .

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