Questions : Run a regression model to estimate the cost of a building using aver
ID: 3047971 • Letter: Q
Question
Questions : Run a regression model to estimate the cost of a building using average storey height (mean centered) and total floor area (mean centered)
question 2: Run a regression model to estimate the cost of a building using average storey height (mean centered), total floor area (mean centered), and the type of construction (dummy coded with reinforced concrete as the control group)
Building type Average floor area (m2) Total floor area (m2) avg story height(cms) COST (HK$) 1 1852 81478 410 1467000000 1 1608 64313 411 1150000000 1 1430 55783 403 1028000000 1 1562 57794 390 1100000000 1 1109 37695 391 728000000 1 905 28048 382 558000000 1 1852 81478 410 1467000000 1 901 30617 391 631000000 1 1727 69062 400 1223000000 1 1161 37148 394 761000000 1 1004 37141 400 713000000 1 1216 38912 390 784000000 1 2007 88302 422 1593000000 1 2983 173000 440 2649000000 2 1523 70080 372 1210000000 2 912 28286 370 607000000 2 1343 53715 382 977000000 2 1175 32908 381 700000000 2 1203 40902 393 811000000 2 1393 52951 392 1001000000 2 713 20681 375 468000000 2 1047 37681 411 747000000 2 1506 63270 421 1156000000 2 1642 70624 423 1268000000 2 1848 73936 403 1333000000 2 1627 60190 402 1162000000 2 1301 40321 384 864000000 2 905 25330 405 561000000 2 1727 72514 400 1303000000 2 1414 52318 392 1013000000 2 2001 76022 431 1487000000 2 400 9200 380 263000000 2 3100 102190 454 2112000000 2 1677 83860 410 1519000000 2 2415 130032 420 2045000000 2 1555 46637 410 1025000000 2 792 20596 420 540000000 Building Type 1 Reinforced Concrete 2 SteelExplanation / Answer
Question 1: Run a regression model to estimate the cost of a building using average storey height (mean centered) and total floor area (mean centered)
Solution:
Required regression model for the estimation of the cost of a building is given as below:
Regression Statistics
Multiple R
0.989851366
R Square
0.979805727
Adjusted R Square
0.978617829
Standard Error
72022022.44
Observations
37
ANOVA
df
SS
MS
F
Significance F
Regression
2
8.557E+18
4.2785E+18
824.82284
0.00
Residual
34
1.76364E+17
5.18717E+15
Total
36
8.73336E+18
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-1007498437
323442007.4
-3.114927604
0.0037239
-1664811677
-350185197.2
Total floor area (m2)
13965.33792
504.2764764
27.69381197
6.543E-25
12940.52482
14990.15101
avg story height(cms)
3185037.528
851125.288
3.742148862
0.0006735
1455342.845
4914732.212
For this regression model, the p-value is given as 0.00 approximately. So we reject the null hypothesis at 5% level of significance. Given regression model by using two independent variables as total floor area and average story height is statistically significant and we can use this regression model for future estimation of the dependent variable cost of a building. The R square value or coefficient of determination for this regression is given as 97.98% which means about 97.98% of the variation in the dependent variable cost is explained by the independent variables.
Question 2: Run a regression model to estimate the cost of a building using average storey height (mean centered), total floor area (mean centered), and the type of construction (dummy coded with reinforced concrete as the control group)
Solution:
Required regression model for the estimation of the cost of a building is given as below:
Regression Statistics
Multiple R
0.990412949
R Square
0.98091781
Adjusted R Square
0.979183065
Standard Error
71063697.67
Observations
37
ANOVA
df
SS
MS
F
Significance F
Regression
3
8.56671E+18
2.85557E+18
565.45375
1.98288E-28
Residual
33
1.66652E+17
5.05005E+15
Total
36
8.73336E+18
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-1034024776
319710997.5
-3.234248381
0.0027704
-1684481688
-383567864.2
Building type
33747823.36
24335169.52
1.386792204
0.1748024
-15762451.04
83258097.77
Total floor area (m2)
14062.25239
502.4502552
27.98735247
1.438E-24
13040.00967
15084.49512
avg story height(cms)
3100861.419
841990.9177
3.682773001
0.0008198
1387818.025
4813904.813
For this regression model, the p-value is given as 0.00 approximately. This means, above regression model is statistically significant and we can use this regression model for the estimation of cost of a building for future use. For this regression model R square value or coefficient of determination is given as 0.9809, which means about 98.09% of the variation in the cost of a building is explained by the independent variables.
Regression Statistics
Multiple R
0.989851366
R Square
0.979805727
Adjusted R Square
0.978617829
Standard Error
72022022.44
Observations
37
ANOVA
df
SS
MS
F
Significance F
Regression
2
8.557E+18
4.2785E+18
824.82284
0.00
Residual
34
1.76364E+17
5.18717E+15
Total
36
8.73336E+18
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
-1007498437
323442007.4
-3.114927604
0.0037239
-1664811677
-350185197.2
Total floor area (m2)
13965.33792
504.2764764
27.69381197
6.543E-25
12940.52482
14990.15101
avg story height(cms)
3185037.528
851125.288
3.742148862
0.0006735
1455342.845
4914732.212
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