13.21 In the Problem 13.9, an agent for a real estate company wanted to predict
ID: 3253331 • Letter: 1
Question
13.21 In the Problem 13.9, an agent for a real estate company wanted to predict the monthly rent for apartments, based o the size of the apartment. The data are stored in RENT. Use the results of that problem.
a. State the coefficient of determination, r 2 , and interpret its meaning. Determine and interpret r and interpret 1-r 2 . b. State the standard error of estimate. Interpret the (Sxy), also. c. How useful do you think this regression model is for predicting the monthly rent?
MonRent Size
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
1750 1200
Explanation / Answer
The statistical software output for regression is:
Simple linear regression results:
Dependent Variable: MonRent
Independent Variable: Size
MonRent = 177.12082 + 1.0651439 Size
Sample size: 25
R (correlation coefficient) = 0.8500608
R-sq = 0.72260336
Estimate of error standard deviation: 194.59539
Parameter estimates:
Analysis of variance table for regression model:
Hence,
a) Coefficient of determination (r2) = 0.7226
It indicates that 72.26% of the variaiton in rent can be explained by the house size.
r = 0.85
It indicates that there is a high association of 0.85 between house size and Rent.
1 - r2 = 1 - 0.7226 = 0.2774
It indicates that 27.74% of the variation in rent is due to factors other than house size.
b) Standard error = 194.60
c) The p - value is almost close to 0 so reject Ho. Hence,
We have sufficient evidence to conclude that this regression model is good for predicting the monthly rent
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 177.12082 161.00428 0 23 1.1001001 0.2827 Slope 1.0651439 0.13760841 0 23 7.7403982 <0.0001Related Questions
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