The accompanying table shows a portion of a data set that refers to the size of
ID: 3228098 • Letter: T
Question
The accompanying table shows a portion of a data set that refers to the size of a home (in square feet) and its property taxes owed by the owner (in $) in an affluent suburb 30 miles outside New York City. a. Determine the sample regression equation that enables us to predict property taxes on the basis of the size of the home. b. Interpret the slope coefficient. As Property Taxes increase by 1 dollar, the size of the house increases by 6.99 ft. As Size increases by 1 square foot, the property taxes are predicted to increase by $6.99. c. Predict the property taxes for a 1, 700-square-foot home.Explanation / Answer
Solution:
The required regression analysis by using excel is given as below:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.764105355
R Square
0.583856994
Adjusted R Square
0.560737938
Standard Error
6583.29377
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
1
1094517885
1094517885
25.25436144
0.000088
Residual
18
780115623.5
43339756.86
Total
19
1874633508
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
5991.827788
3951.889312
1.516193222
0.146835712
-2310.783555
14294.43913
size
6.993424987
1.391623407
5.025371772
8.78836E-05
4.069732704
9.917117271
Part a
The required regression equation is given as below:
Property Taxes = 5991.83 + 6.99*Size
Part b
Interpretation of slope
As size increases by 1 square foot, the property taxes are predicted to increase by $6.99.
Part c
Here, we are given size = 1700 square foot
Property Taxes = 5991.83 + 6.99*Size
Property Taxes = 5991.83 + 6.99*1700
Estimate for property taxes = 17874.83
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.764105355
R Square
0.583856994
Adjusted R Square
0.560737938
Standard Error
6583.29377
Observations
20
ANOVA
df
SS
MS
F
Significance F
Regression
1
1094517885
1094517885
25.25436144
0.000088
Residual
18
780115623.5
43339756.86
Total
19
1874633508
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
5991.827788
3951.889312
1.516193222
0.146835712
-2310.783555
14294.43913
size
6.993424987
1.391623407
5.025371772
8.78836E-05
4.069732704
9.917117271
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