Question

An agent for a residential real estate company in a suburb located outside of Washington, DC, has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 48 one-bedroom apartments and collects and stores the data here. What are the values for (1) the proportion of variation in the monthly rental cost that is explained by the size of an apartment , (2) the sum of squares Y , (3) the sum of squares predicted , (4) the sum of squares error , (5) the intercept A , (6) the slope b , (7) the predicted monthy rental cost for an apartment that has 800 square feet and (8) the standard error of estimate ?

Size( Square feet)	Rent($)
524	1110
616	1175
666	1190
830	1410
450	1210
550	1225
780	1480
815	1490
1070	1495
610	1680
835	1810
660	1625
590	1469
675	1395
744	1150
820	1140
912	1220
628	1434
645	1519
840	1105
800	1130
804	1250
950	1449
800	1168
787	1224
960	1391
750	1145
690	1093
840	1353
850	1530
965	1650
1060	1740
665	1235
775	1550
960	1545
827	1583
655	1575
535	1310
625	1195
749	1200
634	1185
641	1444
860	1385
740	1275
593	1050
880	1650
895	1340
692	1560

Answer 1

We first input the data set into MS Excel. We use the Regression option under Data > Data Analysis to carry out the regression analysis. The data set and the corresponding output is given below. From the output we get the answers to our questions.


(1) Proportion of variation = R square = 0.126
(2) Sum of squares Y = SS(Total) = 1820676.979
(3) Sum of squares predicted = SS(Regression) = 228565.193
(4) Sum of squares error = SS(Residual) = 1592111.786
(5) Intercept A = 992.993
(6) Slope b = 0.493
(7) For 800 square feet, predicted monthly rental cost = 992.993 + (0.493 * 800) = 1387.526
(8) Standard error of estimate = Standard error = 186.041