In: Math
The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.
21918 | 2359 |
17318 | 2340 |
18284 | 1936 |
15624 | 1094 |
43998 | 5664 |
33670 | 2577 |
15158 | 2139 |
16691 | 1856 |
18278 | 2052 |
16070 | 1357 |
15181 | 1222 |
36077 | 3110 |
31037 | 2782 |
42061 | 3446 |
14365 | 1524 |
38971 | 3976 |
25313 | 4014 |
22984 | 2332 |
16210 | 3586 |
29229 | 2807 |
a. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)
Taxesˆ = _____ + _____Size.
b. Interpret the slope coefficient.
As Size increases by 1 square foot, the property taxes are predicted to increase by $6.85.
As Property Taxes increase by 1 dollar, the size of the house increases by 6.85 ft.
c. Predict the property taxes for a 1,200-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Taxesˆ
a) Consider the variables
Y : Property taxes
X : Size of home.
The simple linear equation Y on X is
y =a + b * x
a = y-intercept
b = slope of line
Y | X | X2 | XY |
21918 | 2359 | 5564881 | 51704562 |
17318 | 2340 | 5475600 | 40524120 |
18284 | 1936 | 3748096 | 35397824 |
15624 | 1094 | 1196836 | 17092656 |
43998 | 5664 | 32080896 | 249204672 |
33670 | 2577 | 6640929 | 86767590 |
15158 | 2139 | 4575321 | 32422962 |
16691 | 1856 | 3444736 | 30978496 |
18278 | 2052 | 4210704 | 37506456 |
16070 | 1357 | 1841449 | 21806990 |
15181 | 1222 | 1493284 | 18551182 |
36077 | 3110 | 9672100 | 112199470 |
31037 | 2782 | 7739524 | 86344934 |
42061 | 3446 | 11874916 | 144942206 |
14365 | 1524 | 2322576 | 21892260 |
38971 | 3976 | 15808576 | 154948696 |
25313 | 4014 | 16112196 | 101606382 |
22984 | 2332 | 5438224 | 53598688 |
16210 | 3586 | 12859396 | 58129060 |
29229 | 2807 | 7879249 | 82045803 |
488437 | 52173 | 159979489 | 1437665009 |
Hence simple linear equation of Y on X is
Taxes ^ = 6559.498 + 6.85 * size
b) Value of slope = 6.85 ( positive)
Interpretation : As size of home increases by 1 square foot, the property taxes are predicted to increase by $ 6.85.
c) Given : x =1200
Estimated value of property taxes
Taxes^ = 6559.498 + 1200 *6.85
= $ 14779.4976.