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, E(y) = β0 + β1x. The results of the simple linear regression are provided below.
y = 96,600 + 22.5x s = 6500 R2 = 0.77 t = 6.1 (for testing β1)
Interpret the value of the coefficient of determination, R2.
◦ There is a moderately strong positive correlation between sale price (y) and GLA (x).
◦ 77% of the total variation in the sample sale prices can be attributed to the linear relationship between GLA (x) and (y).
◦ GLA (x) is linearly related to sale price (y) 77% of the time.
◦ 77% of the observed sale prices (y's) will fall within 2 standard deviations of the least squares line.
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