4-24 Use the data in Problem 4-22 and develop a regression model to predict sell
ID: 3150578 • Letter: 4
Question
4-24 Use the data in Problem 4-22 and develop a regression model to predict selling price based on the square footage, number of bedrooms, and age. Use this to predict the selling price of a 10-year-old, 2,000-square -foot house with three bedrooms.
4-22:
Below are the 5 questions I have to answer along with the questions above.
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.
4-24: (This is my progress so far) Please critique and correct)
Selling Price Square Footage Bedrooms Age (years) Square Footage: 84000 1670 2 30 SUMMARY OUTPUT 79000 1339 2 25 91500 1712 3 30 Regression Statistics 120000 1840 3 40 Multiple R 0.83664028 127500 2300 3 18 R Square 0.699966957 132500 2234 3 30 Adjusted R Square 0.679964754 145000 2311 3 19 Standard Error 21360.30433 164000 2377 3 7 Observations 17 155000 2736 4 10 168000 2500 3 1 ANOVA 172500 2500 4 3 df SS MS F Significance F 174000 2479 3 3 Regression 1 15966678629 15966678629 34.99449349 2.8346E-05 175000 2400 3 1 Residual 15 6843939018 456262601.2 177500 3124 4 0 Total 16 22810617647 184000 2500 3 2 195500 4062 4 10 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 195000 2854 3 3 Intercept 26532.23614 21408.35529 1.239340238 0.23426098 -19098.593 72163.06528 -19098.593 72163.06528 X Variable 1 51.02721153 8.625851561 5.91561438 2.8346E-05 32.64164414 69.41277892 32.64164414 69.41277892 Selling Price= 26532.23614+51.02721153*square footage Bedrooms: SUMMARY OUTPUT Regression Statistics Multiple R 0.658191861 R Square 0.433216526 Adjusted R Square 0.395430961 Standard Error 29358.3391 Observations 17 ANOVA df SS MS F Significance F Regression 1 9881936525 9881936525 11.46513294 0.004072954 Residual 15 12928681122 861912074.8 Total 16 22810617647 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 20331.63265 38780.77643 0.524270902 0.60775107 -62327.63564 102990.9009 -62327.63564 102990.9009 X Variable 1 41403.06122 12227.64736 3.386020222 0.004072954 15340.44782 67465.67463 15340.44782 67465.67463 Selling Price= 20331.63265+41403.06122*number of bedrooms Age: SUMMARY OUTPUT Regression Statistics Multiple R 0.838264965 R Square 0.702688152 Adjusted R Square 0.682867362 Standard Error 21263.21846 Observations 17 ANOVA df SS MS F Significance F Regression 1 16028750756 16028750756 35.45207613 2.64302E-05 Residual 15 6781866891 452124459.4 Total 16 22810617647 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 182504.7044 7581.975131 24.0708656 2.12134E-13 166344.1069 198665.3018 166344.1069 198665.3018 X Variable 1 -2424.91368 407.2634606 -5.9541646 2.64302E-05 -3292.975199 -1556.85216 -3292.975199 -1556.852163 Selling Price= 182504.7044-2424.91368*AgeExplanation / Answer
Regression Analysis
R²
0.868
Adjusted R²
0.837
n
17
R
0.932
k
3
Std. Error
15231.904
Dep. Var.
Selling Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
19,794,476,008.2741
3
6,598,158,669.4247
28.44
5.56E-06
Residual
3,016,141,638.7847
13
232,010,895.2911
Total
22,810,617,647.0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
91,446.4930
26,076.8905
3.507
.0039
35,110.7961
147,782.1898
Square Footage
29.8579
10.8609
2.749
.0166
6.3943
53.3214
Bedrooms
2,116.8554
10,003.0092
0.212
.8357
-19,493.3321
23,727.0430
Age (years)
-1,504.7659
370.8204
-4.058
.0014
-2,305.8746
-703.6572
Use this to predict the selling price of a 10-year-old, 2,000-square -foot house with three bedrooms.
Price (P)= 91,446.4930 + 29.8579 *Square Foot + 2,116.8554 *Bedrooms -1,504.7659 *Age
Predicted Price (P) = 91,446.4930 + 29.8579 *2000 + 2,116.8554 *3 -1,504.7659 *10
=142465.2002
Predicted Price (P)=$142465.20
Below are the 5 questions I have to answer along with the questions above.
1.State the linear equation.
Price (P)= intercept + b 1*Square Foot + b 2*Bedrooms + b3*Age
Price (P)= 91,446.4930 + 29.8579 *Square Foot + 2,116.8554 *Bedrooms -1,504.7659 *Age
2.Explain the overall statistical significance of the model.
Calculated F=28.44 , P=0.000 which is < 0.05 level of significance.
The null hypothesis is rejected.
The model is significant.
3.Explain the statistical significance for each independent variable in the model
For the variable Square Footage, t=2.749, P=0.0166 which is < 0.05 level. The Square Footage is significant.
For the variable Bedrooms, t=0.212, P=0.8357 which is > 0.05 level. The Bedrooms is not significant.
For the variable Age (years), t=-4.058 which is < 0.05 level. The Age (years)is significant.
4.Interpret the Adjusted R2.
Adj. R2 =0.834
83.4% of variance in price is explained by the regression model.
5.Is this a good predictive equation(s)? Which variables should be excluded (if any) and why? Explain.
Since the model is significant, this is a good predictive equation.
Since the variable Bedrooms is not significant, this should be excluded from the model.
Regression Analysis
R²
0.868
Adjusted R²
0.837
n
17
R
0.932
k
3
Std. Error
15231.904
Dep. Var.
Selling Price
ANOVA table
Source
SS
df
MS
F
p-value
Regression
19,794,476,008.2741
3
6,598,158,669.4247
28.44
5.56E-06
Residual
3,016,141,638.7847
13
232,010,895.2911
Total
22,810,617,647.0588
16
Regression output
confidence interval
variables
coefficients
std. error
t (df=13)
p-value
95% lower
95% upper
Intercept
91,446.4930
26,076.8905
3.507
.0039
35,110.7961
147,782.1898
Square Footage
29.8579
10.8609
2.749
.0166
6.3943
53.3214
Bedrooms
2,116.8554
10,003.0092
0.212
.8357
-19,493.3321
23,727.0430
Age (years)
-1,504.7659
370.8204
-4.058
.0014
-2,305.8746
-703.6572
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