Using any of the independent variables, create and report the best fitting linea
ID: 3132855 • Letter: U
Question
Using any of the independent variables, create and report the best fitting linear model to predict the selling price of the house. Use the following criteria to make your decision:
Significance of the overall model
Significance of the coefficients
Coefficient of Determination
Standard Error of the Regression
Explain why you chose the linear equation you did and use those criteria to support your decision.
Price Bedrooms Size Pool Distance Garage Baths Twnship 263.1 4 2300 1 17 1 2 5 182.4 4 2100 0 19 0 2 4 242.1 3 2300 0 12 0 2 3 213.6 2 2200 0 16 0 2.5 2 139.9 2 2100 0 28 0 1.5 1 245.4 2 2100 1 12 1 2 1 327.2 6 2500 0 15 1 2 3 271.8 2 2100 0 9 1 2.5 2 221.1 3 2300 1 18 0 1.5 1 266.6 4 2400 0 13 1 2 4 292.4 4 2100 0 14 1 2 3 209 2 1700 0 8 1 1.5 4 270.8 6 2500 0 7 1 2 4 246.1 4 2100 0 18 1 2 3 194.4 2 2300 0 11 0 2 3 281.3 3 2100 0 16 1 2 2 172.7 4 2200 1 16 0 2 3 207.5 5 2300 1 21 0 2.5 4 198.9 3 2200 1 10 1 2 4 209.3 6 1900 1 15 1 2 4 252.3 4 2600 0 8 1 2 4 192.9 4 1900 1 14 1 2.5 2 209.3 5 2100 0 20 0 1.5 5 345.3 8 2600 0 9 1 2 4 326.3 6 2100 0 11 1 3 5 173.1 2 2200 1 21 1 1.5 5 187 2 1900 0 26 0 2 4 257.2 2 2100 0 9 1 2 4 233 3 2200 0 14 1 1.5 3 180.4 2 2000 0 11 0 2 5 234 2 1700 0 19 1 2 3 207.1 2 2000 0 11 1 2 5 247.7 5 2400 0 16 1 2 2 166.2 3 2000 1 16 1 2 2 177.1 2 1900 0 10 1 2 5 182.7 4 2000 1 14 0 2.5 4 216 4 2300 0 19 0 2 2 312.1 6 2600 0 7 1 2.5 5 199.8 3 2100 0 19 1 2 3 273.2 5 2200 0 16 1 3 2 206 3 2100 1 9 0 1.5 3 232.2 3 1900 1 16 1 1.5 1 198.3 4 2100 1 19 1 1.5 1 205.1 3 2000 1 20 0 2 4 175.6 4 2300 1 24 1 2 4 307.8 3 2400 1 21 1 3 2 269.2 5 2200 0 8 1 3 5 224.8 3 2200 0 17 1 2.5 1 171.6 3 2000 1 16 0 2 4 216.8 3 2200 0 15 1 2 1 192.6 6 2200 1 14 0 2 1 236.4 5 2200 0 20 1 2 3 172.4 3 2200 0 23 0 2 3 251.4 3 1900 0 12 1 2 2 246 6 2300 0 7 1 3 3 147.4 6 1700 1 12 0 2 1 176 4 2200 0 15 1 2 1 228.4 3 2300 0 17 1 1.5 5 166.5 3 1600 1 19 0 2.5 3 189.4 4 2200 0 24 1 2 1 312.1 7 2400 0 13 1 3 3 289.8 6 2000 0 21 1 3 3 269.9 5 2200 1 11 1 2.5 4 154.3 2 2000 0 13 0 2 2 222.1 2 2100 0 9 1 2 5 209.7 5 2200 1 13 1 2 2 190.9 3 2200 1 18 1 2 3 254.3 4 2500 1 15 1 2 3 207.5 3 2100 1 10 0 2 2 209.7 4 2200 1 19 1 2 2 294 2 2100 0 13 1 2.5 2 176.3 2 2000 1 17 0 2 3 294.3 7 2400 0 8 1 2 4 224 3 1900 1 6 1 2 1 125 2 1900 0 18 0 1.5 4 236.8 4 2600 1 17 1 2 5 164.1 4 2300 0 19 0 2 4 217.8 3 2500 0 12 0 2 3 192.2 2 2400 0 16 0 2.5 2 125.9 2 2400 0 28 0 1.5 1 220.9 2 2300 1 12 1 2 1 294.5 6 2700 0 15 1 2 3 244.6 2 2300 0 9 1 2.5 2 199 3 2500 1 18 0 1.5 1 240 4 2600 0 13 1 2 4 263.2 4 2300 0 14 1 2 3 188.1 2 1900 0 8 1 1.5 4 243.7 6 2700 0 7 1 2 4 221.5 4 2300 0 18 1 2 3 175 2 2500 0 11 0 2 3 253.2 3 2300 0 16 1 2 2 155.4 4 2400 1 16 0 2 3 186.7 5 2500 1 21 0 2.5 4 179 3 2400 1 10 1 2 4 188.3 6 2100 1 15 1 2 4 227.1 4 2900 0 8 1 2 4 173.6 4 2100 1 14 1 2.5 2 188.3 5 2300 0 20 0 1.5 5 310.8 8 2900 0 9 1 2 4 293.7 6 2400 0 11 1 3 5 179 3 2400 0 8 1 2 4 188.3 6 2100 1 14 1 2.5 2 227.1 4 2900 0 20 0 1.5 5 173.6 4 2100 0 9 1 2 4 188.3 5 2300 0 11 1 3 5Explanation / Answer
Using any of the independent variables, create and report the best fitting linear model to predict the selling price of the house. Use the following criteria to make your decision:
Solution:
The regression model for the prediction of the selling price of the house is given as below:
Regression Analysis
Regression Statistics
Multiple R
0.6204
R Square
0.3849
Adjusted R Square
0.3538
Standard Error
37.8652
Observations
105
ANOVA
df
SS
MS
F
Significance F
Regression
5
88823.9147
17764.7829
12.3902
0.0000
Residual
99
141943.6744
1433.7745
Total
104
230767.5891
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
63.7500
44.5294
1.4316
0.1554
-24.6060
152.1060
Bedrooms
8.2762
2.8797
2.8740
0.0050
2.5623
13.9902
Size
0.0458
0.0164
2.7884
0.0064
0.0132
0.0784
Distance
-2.2898
0.7962
-2.8759
0.0049
-3.8697
-0.7099
Baths
29.3405
10.2173
2.8716
0.0050
9.0671
49.6139
Twnship
-1.1316
3.0191
-0.3748
0.7086
-7.1221
4.8589
Significance of the overall model
For the purpose of the prediction of the selling price of the house, we assume the level of significance or the alpha value as 0.05 or 5%.
Significance of the coefficients
For this regression analysis, we get the multiple correlation coefficient as 0.6204, which means, there is a considerably high positive linear relationship exists between the dependent variable price of the house and independent variables such as number of bedrooms, size, distance, baths, township, etc.
Coefficient of Determination
The value of the R square or the coefficient of determination for this regression model is given as 0.3849, this means about 38.49% of the variation in the dependent variable price of the house is explained by the independent variables such as number of bedrooms, size, distance, baths, township, etc.
Standard Error of the Regression
The standard error for this regression analysis is given as 37.8652 which we consider during the prediction or estimation of the price of the house.
Explain why you chose the linear equation you did and use those criteria to support your decision.
It is observed that there is a linear relationship exists between the pairs of the variables so we choose the linear equation for the regression analysis. For this regression model, we get the p-value as 0.00 which is less than the given level of significance 0.05, so we reject the null hypothesis that the given regression model is significant.
Regression Analysis
Regression Statistics
Multiple R
0.6204
R Square
0.3849
Adjusted R Square
0.3538
Standard Error
37.8652
Observations
105
ANOVA
df
SS
MS
F
Significance F
Regression
5
88823.9147
17764.7829
12.3902
0.0000
Residual
99
141943.6744
1433.7745
Total
104
230767.5891
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
63.7500
44.5294
1.4316
0.1554
-24.6060
152.1060
Bedrooms
8.2762
2.8797
2.8740
0.0050
2.5623
13.9902
Size
0.0458
0.0164
2.7884
0.0064
0.0132
0.0784
Distance
-2.2898
0.7962
-2.8759
0.0049
-3.8697
-0.7099
Baths
29.3405
10.2173
2.8716
0.0050
9.0671
49.6139
Twnship
-1.1316
3.0191
-0.3748
0.7086
-7.1221
4.8589
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