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 | 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.
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]