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In: Economics

Appraised Value Property Size Age 467.8 0.2249 44 363.9 0.2169 56 429.9 0.1631 27 540.5 0.4672...

Appraised Value Property Size Age
467.8 0.2249 44
363.9 0.2169 56
429.9 0.1631 27
540.5 0.4672 18
405.8 0.2523 47
375.2 0.2214 86
318.2 0.1864 46
748.4 0.5062 7
212.8 0.2274 59
632.4 0.1385 13
349.4 0.1749 58
356.5 0.4216 49
359.6 0.2518 43
273.9 0.1158 17
303.8 0.1685 62
280.9 0.1746 58
390.4 0.3873 46
617.5 0.6578 47
313.9 0.1718 58
361.8 0.1425 75

1. Construct a​ 95% confidence interval estimate for the the mean appraised value for houses that have a land area of 0.15 acres and is 35 years old.

2. Construct a​ 95% prediction interval estimate for the the mean appraised value for houses that have a land area of 0.15 acres and is 35 years old.

Need process.

Solutions

Expert Solution

It shall be noted that regression of Appraisal Value on Property Size and Age is given as follows, as estimated using Excel - Data Analysis Tool Pack based Regression

1)

Using the data analysis tool pack - Descriptive statistics, compute the descriptive summary of the variable - Appraisal value

Appraised Value
Mean 405.13
Standard Error 30.15225147
Median 362.85
Mode #N/A
Standard Deviation 134.8449679
Sample Variance 18183.16537
Kurtosis 1.071007329
Skewness 1.197199183
Range 535.6
Minimum 212.8
Maximum 748.4
Sum 8102.6
Count 20
Confidence Level(95.0%) 63.10938761

The mean value is 405.13 and the confidence level (95%) is 63.10938761

Hence, the 95% confidence interval estimate for the mean of the appraised value for house is given as:

Lower Limit = 405.13 - 63.10938761 = 342.0206124

Upper Limit = 405.13 + 63.10938761 = 468.2393876

Thus, 95% confidence interval estimate is [342.0206124 , 468.2393876]

2)

Estimate the regression of Appraised value on Property Size and Age of the House.

The result is:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.761188758
R Square 0.579408326
Adjusted R Square 0.529926952
Standard Error 92.45223613
Observations 20
ANOVA
df SS MS F Significance F
Regression 2 200174.0706 100087.0353 11.70962496 0.000635061
Residual 17 145306.0714 8547.415965
Total 19 345480.142
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 428.6181491 73.52043378 5.829918664 2.00871E-05 273.5035926 583.7327055 273.5035926 583.7327055
Property Size 449.8693026 150.5123253 2.988920021 0.008247175 132.3160539 767.4225512 132.3160539 767.4225512
Age -3.101505555 1.06908272 -2.901090342 0.009939578 -5.357072932 -0.845938177 -5.357072932 -0.845938177

The Predicted value of Appraised value at 0.15 land size and 35 years as age of house is:

428.6181491 + 449.8693026*0.15 + (-3.101505555*35) = 492.9970389

Using the 95% coefficient of Intercept, Property Size and Age , compute the Lower Prediction Limit as given below:

273.5035926 + 132.3160539*0.15 + (-5.357072932*35) = 105.8534481

Using the 95% coefficient of Intercept, Property Size and Age , compute the Upper Prediction Limit as given below:

583.7327055 + 767.4225512*0.15 + (-0.845938177*35) = 669.238252

Thus, 95% prediction interval estimate is [105.8534481 , 669.238252]

Rahul Sunny answered 9 months ago
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