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 b0 = 268.7900 and b1 = 0.9432. Complete parts (a) and (b).

a. Determine the coefficient of determination, r2, and interpret its meaning.

r2 = ?

b. Determine the standard error of the estimate, SYX, and interpret its meaning.

SYX = ?

Monthly Rent ($) 950 1,500 820 1,600 1,900 925 1,750 1,400 Size (Square Feet) 850 1,350 950 1,100 1,900 750 1,300 1,050

Explanation / Answer

a) coefficient of determination, r2, = 0.7142 and it means 71.42% variation in Size can be explained by the variation in Monthly Rent.

b) SYX = 236.1825

SUMMARY OUTPUT Regression Statistics Multiple R 0.845132 R Square 0.714248 Adjusted R Square 0.666623 Standard Error 236.1825 Observations 8 ANOVA df SS MS F Significance F Regression 1 836578.9 836578.9 14.99725 0.008241 Residual 6 334693 55782.16 Total 7 1171272 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 257.3239 295.6437 0.870385 0.417548 -466.09 980.738 -466.09 980.738 X Variable 1 0.949882 0.245281 3.872628 0.008241 0.349701 1.550063 0.349701 1.550063

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