Question

The following data set is adapted from current Raleigh real estate listings for zip code 27605, near NCSU.

(a) Using Excel, enter the following data set:

BEDROOM (x1)	BATHROOM (x2)	SQ.FT (x3)	PRICE (P)
1	1	500	$67500
1	1	800	$128000
1	1	800	$128000
2	1.5	948	$138000
2	1	904	$145000
2	2	1125	$154900
2	1.5	1050	$156000
2	2	1265	$158500
2	2	1010	$164900
2	2.5	1140	$171000
2	2	1150	$173000
4	1.5	2540	$289900

(b) Use LINEST to find a linear price function for the above data. (Note: You will be using the format (Price = b + m1*x1 + m2*x2 + m3*x3) where Price = P(x1, x2, x3) and the values for b, m1, m2, and m3 are all numerical values. These numerical values should be entered correctly to 2 decimal places.)
P(x1, x2, x3) =  +  *x1 +  *x2 +  *x3

(c) Use the UNROUNDED values for b and the three UNROUNDED slopes to predict the price of each listing (rounding the values will greatly affect your results and you will likely get the answers incorrect if you round). (In other words, add an additional column to your spreadsheet and label it "Predicted Price." Enter a formula to perform this function and fill down.) Then, use these values to calculate the error of the prediction. (Again, add an additional column and label it "Error (%)". Enter a formula and fill down.) Enter the values that you find in the table below. The numerical values in the table should be entered correctly to 2 decimal places.

BR	BATH	SQ.FT	$$	PREDICTED PRICE	ERROR (%)
1	1	500	$67500	$	%
1	1	800	$128000	$118603.03	%
1	1	800	$128000	$	-7%
2	1.5	948	$138000	$142929.16	%
2	1	904	$145000	$	-7%
2	2	1125	$154900	$162382.59	%
2	1.5	1050	$156000	$	-3%
2	2	1265	$158500	$174312.14	%
2	2	1010	$164900	$	-7%
2	2.5	1140	$171000	$168031.82	%
2	2	1150	$173000	$	-5%
4	1.5	2540	$289900	$	%

(d) Repeat (a) - (c) when the lowest and highest priced houses are removed.

New linear price function
P(x1, x2, x3) =  +  *x1 +  *x2 +  *x3

New prediction and error table. (Remember not to round the values within your calculation.)

BR	BATH	SQ.FT	$$	PREDICTED PRICE	ERROR (%)
1	1	800	$128000	$128000.00	%
1	1	800	$128000	$	0%
2	1.5	948	$138000	$150417.42	%
2	1	904	$145000	$	-3%
2	2	1125	$154900	$161691.83	%
2	1.5	1050	$156000	$	-3%
2	2	1265	$158500	$163500.04	%
2	2	1010	$164900	$	-3%
2	2.5	1140	$171000	$170873.87	%
2	2	1150	$173000	$	-6%

(e) The largest error from the first data fitting was  %.
The largest error from the second data fitting was  %.

Answer 1

The detailed solution (excel file) can be found at this link ...

https://drive.google.com/open?id=1sqHWarFtjGCm5bkfECOUsSl-81tbNu9g