The following data give the selling price, square footage, number of bedrooms, a
ID: 3153866 • Letter: T
Question
The following data give the selling price, square footage, number of bedrooms, and age of the houses that have sold in a neighborhood in the past 6 months. 1) State the Linear Equation 2) Explain the overall statistical significance of the model 3) Explain the statistical significance for each independent variable in the model 4) Interpret the Adjusted R2 5) IS this a good predictive equation(s)? Which variables should be excluded (if any) and Why? Explain
Selling Price Square Footage Bedrooms Age (years) 84,000 1,670 2 30 79,000 1,339 2 25 91,500 1,712 3 30 120,000 1,840 3 40 127,500 2,300 3 18 132,500 2,234 3 30 145,000 2,311 3 19 164,000 2,377 3 7 155,000 2,736 4 10 168,000 2,500 3 1 172,500 2,500 4 3 174,000 2,479 3 3 175,000 2,400 3 1 177,500 3,124 4 0 184,000 2,500 3 2 195,500 4,062 4 10 195,000 2,854 3 3Explanation / Answer
Solution:
The regression analysis is given as below:
Regression Analysis
Regression Statistics
Multiple R
0.9315
R Square
0.8678
Adjusted R Square
0.8373
Standard Error
15231.9039
Observations
17
ANOVA
df
SS
MS
F
Significance F
Regression
3
19794476008.2741
6598158669.4247
28.4390
0.0000
Residual
13
3016141638.7847
232010895.2911
Total
16
22810617647.0588
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
91446.4930
26076.8905
3.5068
0.0039
35110.7962
147782.1897
Square Footage
29.8579
10.8609
2.7491
0.0166
6.3943
53.3214
Bedrooms
2116.8554
10003.0092
0.2116
0.8357
-19493.3321
23727.0430
Age (years)
-1504.7659
370.8204
-4.0579
0.0014
-2305.8746
-703.6572
1) State the Linear Equation
Solution:
The linear equation is given as below:
Selling price = 91446.4930 + 29.8579*square footage + 2116.8554*bedrooms – 1504.7659*age
2) Explain the overall statistical significance of the model
Solution:
The p-value for this regression model is given as 0.00 which is less than the given level of significance so we reject the null hypothesis that there is no any linear relationship exists between the dependent variable selling price and independent variables square footage, number of bedrooms and age.
3) Explain the statistical significance for each independent variable in the model
Solution:
For the variable bedrooms, the p-value is greater than 0.05, so this variable is not significant. Other two variables square footage and age are significant as the p-values for these variables is less than the given level of significance.
4) Interpret the Adjusted R2
Solution:
The adjusted R square or adjusted coefficient of determination is given as 0.8373 which means about 83.73% of the variation in the dependent variable selling price is explained by the independent variables square footage, number of bedrooms and age.
5) IS this a good predictive equation(s)? Which variables should be excluded (if any) and Why? Explain
Solution:
This is not a good predictive equation. The variable number of bedrooms should be excluded because this variable is not significant as the p-value is greater than the given level of significance.
Regression Analysis
Regression Statistics
Multiple R
0.9315
R Square
0.8678
Adjusted R Square
0.8373
Standard Error
15231.9039
Observations
17
ANOVA
df
SS
MS
F
Significance F
Regression
3
19794476008.2741
6598158669.4247
28.4390
0.0000
Residual
13
3016141638.7847
232010895.2911
Total
16
22810617647.0588
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
91446.4930
26076.8905
3.5068
0.0039
35110.7962
147782.1897
Square Footage
29.8579
10.8609
2.7491
0.0166
6.3943
53.3214
Bedrooms
2116.8554
10003.0092
0.2116
0.8357
-19493.3321
23727.0430
Age (years)
-1504.7659
370.8204
-4.0579
0.0014
-2305.8746
-703.6572
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.