Question

In: Statistics and Probability

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.

Taxes Size
21922 2446
17362 2521
18285 1732
15662 1039
43973 5633
33629 2523
15195 2163
16693 1938
18247 2061
16036 1267
15163 1306
36002 3034
31043 2880
42063 3376
14432 1491
38914 3943
25383 3930
22991 2390
16236 3511
29263 2828

Predict the property taxes for a 1,500-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Solutions

Expert Solution

Size (X) Taxes (Y) X * Y X2 Y2
2446 21922 53621212 5982916 480574084
2521 17362 43769602 6355441 301439044
1732 18285 31669620 2999824 334341225
1039 15662 16272818 1079521 245298244
5633 43973 247699909 31730689 1933624729
2523 33629 84845967 6365529 1130909641
2163 15195 32866785 4678569 230888025
1938 16693 32351034 3755844 278656249
2061 18247 37607067 4247721 332953009
1267 16036 20317612 1605289 257153296
1306 15163 19802878 1705636 229916569
3034 36002 109230068 9205156 1296144004
2880 31043 89403840 8294400 963667849
3376 42063 142004688 11397376 1769295969
1491 14432 21518112 2223081 208282624
3943 38914 153437902 15547249 1514299396
3930 25383 99755190 15444900 644296689
2390 22991 54948490 5712100 528586081
3511 16236 57004596 12327121 263607696
2828 29263 82755764 7997584 856323169
Total 52012 488494 1430883154 158655946 13800257592

Equation of regression line is Ŷ = a + bX


b = 6.8611
a =( Σ Y - ( b * Σ X) ) / n
a =( 488494 - ( 6.8611 * 52012 ) ) / 20
a = 6581.6957
Equation of regression line becomes Ŷ = 6581.6957 + 6.8611 X


When X = 1500
Ŷ = 6581.696 + 6.861 X
Ŷ = 6581.696 + ( 6.861 * 1500 )
Ŷ = 16873.20

orchestra answered 1 year ago
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