A real estate magazine reported the results of a regression analysis designed to

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 sales price is GLA, gross living area(x), measured in square feet. Data for 157 properties were used to ft the model, E(y) = beta_0 + beta_1 x. The results of the simple linear regression are provided below. y = 96, 600 + 225x s = 6500 R^2 = 0.77 t = 6.1 (for testing beta_1) interpret the value of the continent of determination, R^3 A. The value of R^2 indicates that GLA (x) in linearly related to sale price (y) 77% of the time. B. The value of R^2 indicates that 7% of the total variation in the sample sale prices can be attributed to the linear relationship between GLA (x) and (y). C. The value of R^3 indicates that 77% of the observed sale prices. (ys) will fall within 2 standard deviations of the least squares line. D. The value of R^2 indicates that there is a moderately strong positive correlation between sale price (y) and GLA (x)

Explanation / Answer

The value of R sqaure tells us how much variation is explained by the independent variable, thus the correct answer is B. ie The value of R sqaure indicates that 77% of the total variation in the sample sale prices xan be attributed to the linear relationship

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