SUMMARY OUTPUT Regression Statistics Multiple R 0.976861736 R Square 0.954258852
ID: 3319699 • Letter: S
Question
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.976861736
R Square
0.954258852
Adjusted R Square
0.941783993
Standard Error
23.845861
Observations
15
ANOVA
df
SS
MS
F
Significance F
Regression
3
130490.1814
43496.73
76.49456
1.1849E-07
Residual
11
6254.875953
568.6251
Total
14
136745.0573
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
1.316523292
54.13092378
-0.02432
0.981032
120.4578832
117.8248
-120.458
117.8248
Sq ft
0.197891211
0.021328742
9.278147
1.55E-06
0.150946965
0.244835
0.150947
0.244835
Lot size
5.064652506
2.218085493
2.283344
0.043281
0.182679252
9.946626
0.182679
9.946626
Baths
8.530415278
15.74230667
-0.54188
0.598707
43.17899864
26.11817
-43.179
26.11817
1. Write the equation to represent the relationship.
2. Using the coefficient of determination, the data a good fit and explain.
3. Explain the quantitative relationship of interest rates to housing starts.
4. Which independent variable is the most significant?
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.976861736
R Square
0.954258852
Adjusted R Square
0.941783993
Standard Error
23.845861
Observations
15
ANOVA
df
SS
MS
F
Significance F
Regression
3
130490.1814
43496.73
76.49456
1.1849E-07
Residual
11
6254.875953
568.6251
Total
14
136745.0573
Explanation / Answer
1) Y' = 1.31652392+0.197891211*Sq ft+ 5.064652506*Lot size + 8.530415278* Baths
2) It is a good fit model. The coefficient of determination explains the percentage of estimated variance.
R-squared value= 0.954258852= 95.42%
3)Y'(interest rates) = 1.31652392+0.197891211*Sq ft+ 5.064652506*Lot size + 8.530415278* Baths
The relationship between sqft and Interest rates are significant. Increase of one squre foot, increases interest rates by 0.19789 unit.
The relationship between Lot size and Interest rates are significant at 0.05 significant level. An increase of Lot size by one unit increases the interest rate by 5.064 units.
The relationship between Baths and Interest rates are not significant at 0.05 significant level. An increase of Baths by one unit increases the interest rate by 8.53 units.
4) Independent variable which are significant to regression.
Sqft is most significant variable with p-value: 1.55*E^-6
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