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)? 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? 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? (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? Property Address Listing Price 7735 S Ash Briar Lane, West Jordan 6627 S Interlochin Lane , West Jordan 3534 W Foxton Circle, West Jordan 2133 W 7560 S, West Jordan 1147 W Bateman Ponds Way, West Jordan 4114 W Millsden lane, West Jordan 6681 S 1570 W, West Jordan 2761 W 8200 S, West Jordan 9087 S Judd Lane, West Jordan 7979 S Lusterpointe Lane, West Jordan 8313 S Garden Creek Ct, West Jordan 4586 Copper Pot Ln, West Jordan 8762 S Terra Pointe Way 301 S Garden Creek Ct, West Jordan 8973 S Galilee Way, West Jordan 2445 W Bueno Vista Dr, West Jordan 9197 Welby Hills Dr, West Jordan 7987 S 3260 W, West Jordan 1231 Woodward Place, West Jordan 1684 Plum Creek Dr, West Jordan 4347 W Wasatch Meadows Dr, West Jordan 8565 S 1380 W, West Jordan 8833 S 1850 W, West Jordan 8897 S 3020 W, West Jordan 4424 W Wasatch Meadows Dr, West Jordan 4285 W 9380 S, West Jordan 9126 Granada Hills Dr, West Jordan 6513 S Luminous Way, West Jordan 8431 S Otter Creek Dr, West Jordan 6493 S Cyclamen Way, West Jordan 6761 S Berault Ct, West Jordan 5935 W Leichen Ave, West Jordan 7946 Hartley Ln, West Jordan 6505 S Luminous Way, West Jordan 6687 W Haven Maple Dr, West Jordan 4996 W 7670 S, West Jordan 5926 W Lillyvale Pl, West Jordan 5302 W Ranches Loop Rd, West Jordan 8378 S Crystal Creek Dr, West Jordan 6468 W Chan Reese Dr, West Jordan 7532 S 4950 W, West Jordan 5434 W Bighorn Cir, West Jordan 6966 W 7895 S, West Jordan 7303 W Flaxton Ln, West Jordan 6982 W Saw Timber Way, West Jordan 7101 W 8170 S, West Jordan 6326 W 8235 S, West Jordan 6414 W Annandale Way, West Jordan 7245 W SilhouetteLn, West Jordan 7313 W Flaxton Ln, West Jordan 6314 W 8680 S, West Jordan 259900 319900 269900 234900 464900 310000 319900 399000 294000 289900 489900 360000 429900 520000 255000 275000 365000 295000 490000 259900 330000 437999 364900 560000 433000 412000 415000 339000 340000 190000 289000 259800 355000 370000 317000 339900 275000 325000 309900 378999 419900 549000 279900 469900 298000 354900 334900 429950 334900 429900 469900 Square Footage 2175 3188 1804 1908 4438 2767 2638 2713 2790 2172 4514 3200 3704 5036 1639 2826 3454 2098 3582 2002 2940 4000 3352 4027 3985 3768 2410 2865 2936 1230 1818 1544 2472 3840 2841 2550 1876 3000 3220 1623 4912 4136 2328 4286 2168 3368 3553 3604 3006 3802 3200 8489 S Ivy Springs Ln, West Jordan 8467 S Delicate Arch Dr, West Jordan 8017 Flaxton Ln, West Jordan 6506 S 5095 W, West Jordan 7181 S Sorrento Way, West Jordan 6496 W 7830 S, West Jordan 6486 W 7830 S, West Jordan 6512 W 7830 S, West Jordan 8422 S Town View Cir, West Jordan 6580 S Solstice Ct, West Jordan 7554 S Wild Oak Dr, West Jordan 6767 Chumard Oak Dr, West Jordan 1267 W Four B Ln, South Jordan 3653 W Snowfield Ct, South Jordan 2529 W Winding Way, South Jordan 10440 S Plum Harvest Way, South Jordan 11503 S 2510 W, South Jordan 10344 S 2840 W, South Jordan 11332 S Portobello Rd, South Jordan 10023 S 3345 W, South Jordan 10473 S Gladys Dr, South Jordan 11178 S Alpine Creek Way, South Jordan 11098 S Becks Bend Ln, South Jordan 11044 S Becks Bend Ln, South Jordan 4444W Enid Dr, South Jordan 9513 S Morywood Ln, South Jordan 1249 W Meadow Ridge Ln, South Jordan 3612 W District Peak Ct, South Jordan 4468 W Glenmore Hills Dr, South Jordan 4429 Sid Dr, South Jordan 9489 S Kirkside Dr, South Jordan 9983 Peach Park Cv, South Jordan 11417 S Jordan Farms Rd, South Jordan 11141 S Aspen Gate Ct, South Jordan 11378 S Via Arboles Ct, South Jordan 3396 W 10235 S, South Jordan 4823 W Crosswater Rd, South Jordan 4904 W Calton Ln, South Jordan 1616 W Becks Bend Ln, South Jordan 11286 S 445 W, South Jordan 2993 W Alta Peak Rd, South Jordan 902 W Hollycrest Dr, South Jordan 4929 W Topcrest Dr, South Jordan 10828 S Lees Dream Dr, South Jordan 10858 S Lees Dream Dr, South Jordan 10099 S 3540 W, South Jordan 527 W Miller Hollow Cv, South Jordan 10998 S Cedarhurst Cv, South Jordan 10258 S Petaluma Way, South Jordan 195000 368900 399900 249900 263900 395322 409950 419875 379800 322500 389900 400000 547100 340000 645000 575000 825000 475000 729000 420000 409900 479900 344950 346950 405000 499900 469900 439900 499000 500000 349900 325000 599900 449900 489000 469900 564900 270000 330950 930000 543210 354900 389900 832020 755719 550000 639000 329900 348900 1457 1500 3663 1952 2856 3212 3604 3692 3800 3504 3246 3524 3459 3080 5940 4457 7002 3642 5529 5285 3800 3945 3013 2983 3700 4910 5051 3446 4056 4400 2856 2400 4824 3890 4365 4384 4526 2394 2621 4042 3071 2766 3200 3794 2643 5317 4922 2764 2854 # of Bedrooms 3 5 3 4 6 4 5 3 5 5 5 6 4 6 5 5 6 4 5 3 6 6 7 4 6 5 5 3 3 2 4 3 4 4 6 5 4 3 2 3 4 5 3 5 4 4 3 4 4 4 3 Class 190000-29 296000-40 402000-50 508000-61 614000-72 720000-82 826,000-93 40 35 30 25 20 15 10 5 0 Frequency Frequency 40 35 30 25 20 15 10 5 0 3 3 6 5 3 4 4 4 4 4 5 5 3 3 7 4 8 6 6 5 5 5 4 4 3 6 6 5 6 5 6 6 5 5 5 6 3 5 3 5 4 4 5 5 3 6 5 3 3 Frequency Relative frequency 18 0.18 38 0.38 28 0.28 9 0.09 2 0.02 3 0.03 2 0.02 0 0 100 Frequency Polygon 40 35 30 25 20 15 10 5 0 Frequency Price range Histogram Frequency 40 35 30 25 20 15 10 5 0 Frequency Price Range bedrooms Frequency 2 3 4 5 6 7 8 Total 2 23 25 29 18 2 1 100 35 29 30 23 25 25 18 20 Frequency 15 10 5 0 2 2 3 4 5 Number of bedrooms 6 Bar Graph 29 18 5 of bedrooms 6 2 1 7 8 Listing Price Square Footage Mean Standard Deviation 409840.94 Mean 134899.449994148 Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 18197861608.7236 Sample Variance 2.8221110206 Kurtosis 1.4396974775 Skewness 740000 Range 190000 Minimum 930000 Maximum 40984094 Sum 100 Count Listing Price 1st Quartile 3rd Quartile Square Footage 324375 1st Quartile 469900 3rd quartile 3346.49 1067.0161974195 1138523.56555556 0.5670730738 0.4897128125 5772 1230 7002 334649 100 2695.5 3955 Property Address Listing Price 7735 S Ash Briar Lane, West Jordan 6627 S Interlochin Lane , West Jordan 3534 W Foxton Circle, West Jordan 2133 W 7560 S, West Jordan 1147 W Bateman Ponds Way, West Jordan 4114 W Millsden lane, West Jordan 6681 S 1570 W, West Jordan 2761 W 8200 S, West Jordan 9087 S Judd Lane, West Jordan 7979 S Lusterpointe Lane, West Jordan 8313 S Garden Creek Ct, West Jordan 4586 Copper Pot Ln, West Jordan 8762 S Terra Pointe Way 301 S Garden Creek Ct, West Jordan 8973 S Galilee Way, West Jordan 2445 W Bueno Vista Dr, West Jordan 9197 Welby Hills Dr, West Jordan 7987 S 3260 W, West Jordan 1231 Woodward Place, West Jordan 1684 Plum Creek Dr, West Jordan 4347 W Wasatch Meadows Dr, West Jordan 8565 S 1380 W, West Jordan 8833 S 1850 W, West Jordan 8897 S 3020 W, West Jordan 4424 W Wasatch Meadows Dr, West Jordan 4285 W 9380 S, West Jordan 9126 Granada Hills Dr, West Jordan 6513 S Luminous Way, West Jordan 8431 S Otter Creek Dr, West Jordan 6493 S Cyclamen Way, West Jordan 6761 S Berault Ct, West Jordan 5935 W Leichen Ave, West Jordan 7946 Hartley Ln, West Jordan 6505 S Luminous Way, West Jordan 6687 W Haven Maple Dr, West Jordan 4996 W 7670 S, West Jordan 5926 W Lillyvale Pl, West Jordan 5302 W Ranches Loop Rd, West Jordan 8378 S Crystal Creek Dr, West Jordan 6468 W Chan Reese Dr, West Jordan 7532 S 4950 W, West Jordan 5434 W Bighorn Cir, West Jordan 6966 W 7895 S, West Jordan 7303 W Flaxton Ln, West Jordan 6982 W Saw Timber Way, West Jordan 7101 W 8170 S, West Jordan 6326 W 8235 S, West Jordan 6414 W Annandale Way, West Jordan 7245 W SilhouetteLn, West Jordan 7313 W Flaxton Ln, West Jordan 6314 W 8680 S, West Jordan 8489 S Ivy Springs Ln, West Jordan 8467 S Delicate Arch Dr, West Jordan 8017 Flaxton Ln, West Jordan 6506 S 5095 W, West Jordan 259900 319900 269900 234900 464900 310000 319900 399000 294000 289900 489900 360000 429900 520000 255000 275000 365000 295000 490000 259900 330000 437999 364900 560000 433000 412000 415000 339000 340000 190000 289000 259800 355000 370000 317000 339900 275000 325000 309900 378999 419900 549000 279900 469900 298000 354900 334900 429950 334900 429900 469900 195000 368900 399900 249900 7181 S Sorrento Way, West Jordan 6496 W 7830 S, West Jordan 6486 W 7830 S, West Jordan 6512 W 7830 S, West Jordan 8422 S Town View Cir, West Jordan 6580 S Solstice Ct, West Jordan 7554 S Wild Oak Dr, West Jordan 6767 Chumard Oak Dr, West Jordan 1267 W Four B Ln, South Jordan 3653 W Snowfield Ct, South Jordan 2529 W Winding Way, South Jordan 10440 S Plum Harvest Way, South Jordan 11503 S 2510 W, South Jordan 10344 S 2840 W, South Jordan 11332 S Portobello Rd, South Jordan 10023 S 3345 W, South Jordan 10473 S Gladys Dr, South Jordan 11178 S Alpine Creek Way, South Jordan 11098 S Becks Bend Ln, South Jordan 11044 S Becks Bend Ln, South Jordan 4444W Enid Dr, South Jordan 9513 S Morywood Ln, South Jordan 1249 W Meadow Ridge Ln, South Jordan 3612 W District Peak Ct, South Jordan 4468 W Glenmore Hills Dr, South Jordan 4429 Sid Dr, South Jordan 9489 S Kirkside Dr, South Jordan 9983 Peach Park Cv, South Jordan 11417 S Jordan Farms Rd, South Jordan 11141 S Aspen Gate Ct, South Jordan 11378 S Via Arboles Ct, South Jordan 3396 W 10235 S, South Jordan 4823 W Crosswater Rd, South Jordan 4904 W Calton Ln, South Jordan 1616 W Becks Bend Ln, South Jordan 11286 S 445 W, South Jordan 2993 W Alta Peak Rd, South Jordan 902 W Hollycrest Dr, South Jordan 4929 W Topcrest Dr, South Jordan 10828 S Lees Dream Dr, South Jordan 10858 S Lees Dream Dr, South Jordan 10099 S 3540 W, South Jordan 527 W Miller Hollow Cv, South Jordan 10998 S Cedarhurst Cv, South Jordan 10258 S Petaluma Way, South Jordan 263900 395322 409950 419875 379800 322500 389900 400000 547100 340000 645000 575000 825000 475000 729000 420000 409900 479900 344950 346950 405000 499900 469900 439900 499000 500000 349900 325000 599900 449900 489000 469900 564900 270000 330950 930000 543210 354900 389900 832020 755719 550000 639000 329900 348900 Square Footage # of Bedrooms 2175 3 3188 5 1804 3 1908 4 4438 6 2767 4 2638 5 2713 3 2790 5 2172 5 4514 5 3200 6 3704 4 5036 6 1639 5 2826 5 3454 6 2098 4 3582 5 2002 3 2940 6 4000 6 3352 7 4027 4 3985 6 3768 5 2410 5 2865 3 2936 3 1230 2 1818 4 1544 3 2472 4 3840 4 2841 6 2550 5 1876 4 3000 3 3220 2 1623 3 4912 4 4136 5 2328 3 4286 5 2168 4 3368 4 3553 3 3604 4 3006 4 3802 4 3200 3 1457 3 1500 3 3663 6 1952 5 The empirical rule applies to normally or bell shaped distributions. Th will likely fall within one standard deviation of the average, more than of the average and more than 98.7% of the collected research will m Chebyshev's theorem on the other hand mostly applies to skewed dis of the mean. Based on this, it dictates that at least 3/4 of the data wil three standard deviations of the mean. THE FOLLOWING WAS OBTAINED FOR THE DATA Listing Price Mean Standard Deviation 409840.94 134899.449994148 2 standard deviations is between 140042.040011704 and Number of house prices within this range= Proportion within this range = 3 standard deviations is between 5142.5900175559 and Number of house prices within the range = Proportion within this range = Square Footage Mean Standard Deviation 3346.49 1067.0161974195 2 standard deviations is between 1212.457605161 and Number of houses within the range = Proportion within this range = 3 standard deviations is between 145.4414077415 and Number of houses within the range = Proportion within this range = 2856 3212 3604 3692 3800 3504 3246 3524 3459 3080 5940 4457 7002 3642 5529 5285 3800 3945 3013 2983 3700 4910 5051 3446 4056 4400 2856 2400 4824 3890 4365 4384 4526 2394 2621 4042 3071 2766 3200 3794 2643 5317 4922 2764 2854 3 4 4 4 4 4 5 5 3 3 7 4 8 6 6 5 5 5 4 4 3 6 6 5 6 5 6 6 5 5 5 6 3 5 3 5 4 4 5 5 3 6 5 3 3 Based on the actual proportions within two and three standard devia our data appears to follow neither the empirical rule nor the chebysh own way ll shaped distributions. The rule states that, for normally distributed data, about over 67% of the research obtained of the average, more than 94% of all of the collected the researched will more likely to fall in two standard deviation collected research will more likely near the three standard deviation of the average. ostly applies to skewed distribution. The rule states that, at least 11/k2 of the data lie within k standard deviations at least 3/4 of the data will lie within two standard deviations of the mean, and at least 8/9 of the data will lie within 679639.839988296 95 0.95 814539.289982444 97 0.97 5480.522394839 97 0.97 6547.5385922585 99 0.99 and three standard deviations for both listing prices and square footage, rical rule nor the chebyshev's theorem. The data is thus unique in its e research obtained wo standard deviation k standard deviations he data will lie within