Chapter: CH4 Problem: 23P show all steps Question: Use the data in Problem 4-22
ID: 447631 • Letter: C
Question
Chapter: CH4 Problem: 23P show all steps Question: Use the data in Problem 4-22 and develop a regression model to predict selling price based on the square footage and number of bedrooms. Use this to predict the selling price of a 2,000-square-foot house with three bedrooms. Compare this model with the models in Problem 4-22. Should the number of bedrooms be CH422Pincluded in the model? Why or why not? CH4 24P Reference Problem 4-22 The following data give the selling price, square footage, number of bedrooms, and age of houses that have sold in a neighborhood in the past 6 months. Develop three regression models to predict the selling price based upon each of the other factors individually. Which of these is best? SELLINGSQUARE PRICE ($) FOOTAGE BEDROOMS (YEARS) AGE 84,000 79,000 91,500 120,000 127,500 132,500 145,000 164,000 155,000 168,000 172,500 174,000 175,000 177,500 184,000 195,500 195,000 1,670 1,339 1,712 1,840 2,300 2,234 2,311 2,377 2,736 2,500 2,500 2,479 2,400 3,124 2,500 4,062 2,854 30 25 30 40 18 30 19 4 10 4 0 4 10 11:42 AM 4/6/2016 0Explanation / Answer
Selling Price Square Foot Bedrooms Age (Y) (X1) (X2) (X3) X1 ^2 X2 ^2 X3 ^2 Y^2 X1Y X2Y X3Y 8400 1670 2 30 2788900 4 900 70560000 14028000 16800 252000 79000 1339 2 25 1792921 4 625 6241000000 105781000 158000 1975000 91500 1712 3 30 2930944 9 900 8372250000 156648000 274500 2745000 120000 1840 3 40 3385600 9 1600 14400000000 220800000 360000 4800000 127500 2300 3 18 5290000 9 324 16256250000 293250000 382500 2295000 132500 2234 3 30 4990756 9 900 17556250000 296005000 397500 3975000 145000 2311 3 19 5340721 9 361 21025000000 335095000 435000 2755000 164000 2377 3 7 5650129 9 49 26896000000 389828000 492000 1148000 155000 2736 4 10 7485696 16 100 24025000000 424080000 620000 1550000 168000 2500 3 1 6250000 9 1 28224000000 420000000 504000 168000 172500 2500 4 3 6250000 16 9 29756250000 431250000 690000 517500 174000 2479 3 3 6145441 9 9 30276000000 431346000 522000 522000 175000 2400 3 1 5760000 9 1 30625000000 420000000 525000 175000 177500 3124 4 0 9759376 16 0 31506250000 554510000 710000 0 184000 2500 3 2 6250000 9 4 33856000000 460000000 552000 368000 195500 4062 4 10 16499844 16 100 38220250000 794121000 782000 1955000 195000 2854 3 3 8145316 9 9 38025000000 556530000 585000 585000 2464400 40938 53 232 1.05E+08 171 5892 395331060000 6303272000 8006300 25785500 Regression Equation = a + Bx a = [(y - bx) / n b = [nxy - (x * y)] / [(n * x^2) - (x^2)] n = 17 r = [nxy - (x * y)] / [(n * x2) - x^2] * [(n * y2) - y^2] Regression Equation between selling price and square footage b = [(17 * 630327200) - (40938 * 2464400)] / (17 * 104715644 - 40938^2) = 60.1271 a = [(2464400 - 60.1271 * 40938) / 17 = 171.555 Y = 171.555 + 60.1271 X1 r = 0.763 r2 = 0.582 Regression Equation between selling price and bedrooms b = [(17 * 8006300) - (53 * 2464400)] / (17 * 171 - 53^2) = 56060.204 a = [(2464400 - 56060.204 * 53) / 17 = -29811.22 Y = -29811.22 + 56060.204 X2 r = 0.690 r2 = 0.476 Regression Equation between selling price and age b = [(17 * 25785500) - (232 * 2464400)] / (17 * 5892 - 232^2) = -2878.449 a = [(2464400 - (-2878.449) * 232) / 17 = 184247.061 Y = 184247.061 - 2878.449 X3 r = -0.77 r2 = 0.593 Relationship between selling price and square footage is best due to the fact that they have highest postive correlation ( r) and coefficient of determination (r^2)