The accompanying table shows a portion of a data set that refers to the size of

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. a. Determine 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.) b. Interpret the slope coefficient As size increases by 1 square foot the property taxes are predicted to increase by $6.74. As Property Taxes increase by 1 dollar, the size of the house increases by 6.74 ft. c. Predict the property taxes for a 1.700-square-foot home. (Round your answer to 2 decimal places.)

Explanation / Answer

a. Line of Regression Y on X i.e Y = bo + b1 X

Mean of X = X / n =    2610.35
Mean of Y = Y / n =   24406.9
(Xi - Mean)^2 =   23387470.5
(Yi - Mean)^2 =   1871754044
(Xi-Mean)*(Yi-Mean) =   157636791.8
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = 157636791.78 / 23387470.5 = 6.74  
bo = Y / n - b1 * X / n  
bo = 24406.9 - 6.74*2610.35 = 6812.56  
Y = bo + b1 X  
Y'=6812.56+6.74*X  

b.

as size increases by 1 square root the proporty taxes are predicted to increase by $6.74

c.Y'=6812.56+6.74*(1700) = 18270.56

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 2426 21981 33984.92 5884990.8 447214.67 2407 17335 41351.22 50011770 1438070.87 1774 18208 699481.32 38426361 5184450.02 1034 15616 2484879.32 77279923 13857535.22 5694 43983 9508897.32 383223691 60365840.77 2402 33600 43409.72 84513088 -1915382.39 2342 15107 72011.72 86488140 2495628.17 1857 16715 567536.22 59165326 5794692.87 2111 18300 249350.42 37294228 3049480.52 1449 16055 1348733.82 69754234 9699479.07 1201 15185 1986267.42 85043440 12996884.77 3130 36017 270036.12 134794422 6033188.47 2729 31054 14077.82 44183938 788678.42 3363 42036 566482.02 310785167 13268542.12 1648 14359 926117.52 100960294 9669596.57 3912 38925 1694292.72 210775228 18897484.87 3991 25318 1906194.42 830103.21 1257910.22 2334 22921 76369.32 2207898.8 410628.47 3,517 16216 822014.22 67090843 -7426279.49 2,886 29207 75982.92 23040960 1323147.57

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