An agent for a real estate company in a large city would like to be able to pred

Question

An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of the apartment, as defined by square footage. A sample of eight apartments in a neighborhood was selected, and the information gathered revealed the data shown below. For these data, the regression coefficients are b_0 = 271.3229 and b_1 = 0.8973. Complete parts (a) through (d). Monthly Rent ($) 925 1, 550 800 1, 500 1, 900 925 1, 800 1, 250 Size (Square Feet) 750 1, 300 1, 050 1, 200 2,000 750 1, 350 1, 050 a. Determine the coefficient of determination, r^2, and interpret its meaning. r^2 = 0.7279 (Round to four decimal places as needed.) What is the meaning of r^2? A. r^2 measures the proportion of variation in apartment size that can be explained by the variation in monthly rent. B. r^2 measures the proportion of variation in monthly rent that can be explained by the variation in apartment size. C. r^2 measures the proportion of variation in apartment size that cannot be explained by the variation in monthly rent. D. r^2 measures the proportion of variation in monthly rent that cannot be explained by the variation in apartment size. b. Determine the standard error of the estimate, S_YX, and interpret its meaning. S_YX = (Round to four decimal places as needed.)

Explanation / Answer

a) Coefficient od determination r^2 will be = 0.7279

b) Option B is Correct

c) Syx = 225.3259

SUMMARY OUTPUT Regression Statistics Multiple R 0.85319 R Square 0.727932 Adjusted R Square 0.682588 Standard Error 225.3259 Observations 8 ANOVA df SS MS F Significance F Regression 1 815056.9 815056.9 16.05335 0.007065 Residual 6 304630.6 50771.77 Total 7 1119688 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 101.268 281.0726 0.360291 0.730973 -586.492 789.0278 -586.492 789.0278 X Variable 1 0.811254 0.202476 4.006663 0.007065 0.315813 1.306696 0.315813 1.306696

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