Real Estate Regression Exercise QNT/351 Version 5 1 University of Phoenix Material Real Estate Regression Exercise Directions: Use the real estate data you used for your Week 2 learning team assignment. Analyze the data and explain your answers. 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. 1. Which variable is the independent variable (x) and which is the dependent variable (y)? ANSWER: The dependent variable is the result of the independent variable. In this case, the square footage is the independent variable and the price, or dependent, variable is the result of the cost of the square footage. Had we been looking at price only, it could be said that price would have been the independent variable and results such as mode, mean, median, etc., would have been considered as dependent variables. 2. Click on any cell. Click on InsertScatterScatter with markers (upper left). To add a trendline, click ToolsLayoutTrendlineLinear Trendline Does the scatterplot indicate observable correlation? If so, does it seem to be strong or weak? In what direction? ANSWER: Should only one cell be chosen with one variable, the scatterplot does not appear to have observable correlation and it appears weak. However, should a few cells be selected with two or more variables, the scatterplot will carry a more observable correlation, appears strong, and has a positive slope or direction. 3. Click on DataData AnalysisRegressionOK. Highlight your data (including your two headings) and input the correct columns into Input Y Range and Input X Range, respectively. Make sure to check the box entitled \"Labels\". (a) What is the Coefficient of Correlation between square footage and listing price? (b) Does your Coefficient of Correlation seem consistent with your answer to #2 above? Why or why not? (c) 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? Copyright 2016 by University of Phoenix. All rights reserved. Real Estate Regression Exercise QNT/351 Version 5 2 (d) Check the coefficients in your summary output. What is the regression equation relating square footage to listing price? (e) Test the significance of the slope. What is your t-value for the slope? Do you conclude that there is no significant relationship between the two variables or do you conclude that there is a significant relationship between the variables? (f) Using the regression equation that you designated in #3(d) above, what is the predicted sales price for a house of 2100 square feet? Copyright 2016 by University of Phoenix. All rights reserved. LIST PRICE SQFT 320500 4369 299500 4151 293500 4075 285500 3884 283500 3884 512500 3700 499743 3700 512000 3670 511820 3669 300500 3649 280000 3548 276500 3548 276500 3532 304500 3450 271500 3426 294500 3303 267500 3286 292500 3249 237000 2900 270500 2890 253500 2862 252500 2796 279500 2770 234000 2710 269500 2704 232000 2702 220000 2690 218000 2678 213500 2678 210000 2678 248267 2601 246500 2598 219000 2555 259500 2540 217700 2539 214000 2539 208500 2539 204000 2539 253500 2508 254500 2446 251500 2446 229900 2409 252400 2401 244000 2401 256400 2378 212000 2352 210000 2323 203500 2323 202000 2323 202000 2323 200000 2323 239400 2302 248942 2271 243400 2271 228000 2271 215500 2271 249500 2247 209400 2213 205000 2213 233400 2152 238500 2141 236500 2134 235400 2130 284765 2111 278765 2111 231145 2093 234400 2087 251400 2069 208000 2050 197000 2037 192500 2037 233500 1974 231500 1974 241400 1942 203000 1901 194500 1901 193000 1901 225400 1867 216500 1867 198000 1847 SUMMARY OUTPUT Regression Statistics Multiple R 0.7160924591 R Square 0.51278841 Adjusted R Square 0.5078168631 Standard Error 46067.940004 Observations 100 ANOVA df Regression Residual Total Intercept SQFT SS 1 218899238397.7 98 207980999430.9 99 426880237828.6 MS F Significance F 899238398 103.14464024 5.5510907E-017 2122255096 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 80373.069699 16591.70626301 4.8441714448 4.75825E-006 47447.3686056 113298.77079 47447.368606 113298.77079 66.628546504 6.5605010082 10.156014978 5.55109E-017 53.6094457681 79.64764724 53.609445768 79.64764724 268265 230400 194000 201000 193000 186500 181000 222400 210500 190000 182500 178000 221400 189000 202000 182000 182000 173500 171000 107400 1843 1790 1736 1703 1703 1703 1703 1652 1652 1651 1651 1651 1584 1580 1576 1480 1442 1442 1442 1033