Question

In: Math

The accompanying table shows a portion of a data set that refers to the property taxes...

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

Solutions

Expert Solution

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.

milcah answered 2 years ago
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