You are consulting for a large real estate firm. You have been asked to construc

Question

You are consulting for a large real estate firm. You have been asked to construct a model that can predict listing prices based on square footages for homes in the city you’ve been researching. You have data on square footages and listing prices for 100 homes.

Which variable is the independent variable (x) and which is the dependent variable (y)?  

What proportion of the variation in listing price is determined by variation in the square footage? What proportion of the variation in listing price is due to other factors?

Price              Feet $335,000.00 2000 $315,000.00 1165 $469,000.00 1905 $425,000.00 1600 $447,500.00 2147 $434,000.00 1969 $319,990.00 1260 $399,000.00 2177 $270,400.00 1048 $310,000.00 1168 $415,000.00 2171 $379,000.00 1868 $414,900.00 2095 $949,900.00 5458 $339,900.00 1119 $699,990.00 2765 $320,000.00 1372 $649,000.00 3177 $799,900.00 4122 $345,000.00 1437 $745,000.00 3475 $548,800.00 3363 $479,000.00 1855 $410,000.00 1945 $449,900.00 2224 $379,999.00 1714 $289,900.00 864 $429,900.00 1924 $299,900.00 874 $530,000.00 2922 $489,900.00 3906 $429,900.00 1883 $389,000.00 1450 $579,000.00 3517 $290,000.00 1440 $639,900.00 3637 $375,000.00 1263 $432,000.00 2532 $375,000.00 1117 $549,900.00 2630 $699,900.00 3415 $424,900.00 1638 $520,000.00 3145 $395,000.00 1176 $950,000.00 4349 $529,950.00 2219 $578,800.00 2541 $429,000.00 2044 $352,000.00 2154 $395,000.00 1548 $340,000.00 1201 $445,000.00 2028 $430,000.00 2240 $899,000.00 3794 $525,000.00 2042 $379,000.00 1656 $629,900.00 3518 $848,000.00 2175 $315,000.00 1148 $345,000.00 1382 $400,000.00 2118 $328,900.00 1122 $269,000.00 884 $699,000.00 3090 $499,000.00 3270 $379,000.00 1356 $279,999.00 1320 $347,000.00 1100 $449,900.00 2270 $279,888.00 1384 $370,000.00 1992 $399,000.00 1339 $528,000.00 3080 $329,900.00 1254 $459,000.00 3186 $238,000.00 480 $511,000.00 2041 $286,000.00 1092 $348,950.00 1721 $489,000.00 2617 $592,000.00 3174 $329,000.00 1446 $288,500.00 1115 $784,999.00 3806 $849,000.00 3566 $299,900.00 1353 $350,000.00 1615 $261,999.00 816 $589,900.00 3789 $399,000.00 1952 $319,500.00 816 $355,000.00 1664 $949,000.00 3580 $515,000.00 2077 $374,900.00 1428 $899,900.00 3314 $419,999.00 1750 $424,500.00 1992 $419,000.00 2261 $315,000.00 960

Explanation / Answer

Price is dependent variable and Feet is independent variable

r^2=0.75 and hence 75% of the variation is due to independent variable i.e. Feet and 25% is due to other factors.

SUMMARY OUTPUT Regression Statistics Multiple R 0.867462203 R Square 0.752490673 Adjusted R Square 0.749939031 Standard Error 85892.53653 Observations 99 ANOVA df SS MS F Significance F Regression 1 2.17567E+12 2.17567E+12 294.9044238 3.60532E-31 Residual 97 7.1562E+11 7377527832 Total 98 2.89129E+12 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 136618.8055 20903.56675 6.535669591 2.94751E-09 95131.01193 178106.5991 95131.01193 178106.5991 x 153.9778652 8.966390531 17.17278148 3.60532E-31 136.1820621 171.7736684 136.1820621 171.7736684

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