Choose the One Alternative That Best Completes the Statement or Answers

question 72

Multiple Choice

Choose the one alternative that best completes the statement or answers the question.
-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, $\mathrm { E } ( \mathrm { y } ) = \beta _ { 0 } + \beta _ { 1 } \mathrm { x }$ . The results of the simple linear regression are provided below.
$$y = 96,600 + 22.5 x \quad s = 6500 \quad R ^ { 2 } = 0.77 \quad t = 6.1 \text { (for testing } \beta _ { 1 } \text { ) }$$
Interpret the value of the coefficient of determination, $\mathrm { R } ^ { 2 }$ .

• A) \(77 \%\) of the total variation in the sample sale prices can be attributed to the linear relationship between GLA \(( x )\) and \(( y )\).
• B) GLA (x) is linearly related to sale price (y) \(77 \%\) of the time.
• C) \(77 \%\) of the observed sale prices (y's) will fall within 2 standard deviations of the least squares line.
• D) There is a moderately strong positive correlation between sale price (y) and GLA (x).

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