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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Definitions:

Labor Demand Curve

A downward-sloping curve that represents how the quantity of labor demanded by employers changes as the wage rate changes.

Purely Competitive

Purely competitive markets are those in which numerous small firms compete against each other, and the price of goods or services is determined by the market with no single participant having significant control over it.

Imperfectly Competitive

Describes markets where individual sellers have some control over the prices due to lack of perfect competition, includes monopolistic competition, oligopoly, and monopoly markets.

Perfectly Competitive Market

A theoretical market structure characterized by many buyers and sellers, free entry and exit, and a homogeneous product, leading to an efficient allocation of resources.