3. The Sunday April 15, 2007 issue of the Houston Chronicle included a section devoted to real estate prices in Houston. In particular, data are presented on the 2006 median price per square foot for 1922 subdivisions. The data (HoustonRealEstate.txt) can be found on the book web site. Interest centers on developing a regression model to predict Y, = 2006 median price per square foot from x\". = %NewHomes (i.e., of the houses that sold in 2006, the percentage that were built in 2005 or 2006) x2, = %F0reclosures (i.e., 0f the houses that sold in 2006, the percentage that were identied as foreclosures) Table 4.3 Data on salaries Years of experience as a full professor Sample size, a, Third quartile ($) 0 17 101,300 2 33 1 1 1,303 4 19 98,000 6 25 124,000 8 18 128,475 12 60 1 17,410 17 58 1 15,825 22 31 134,300 28 34 128,066 34 19 164,700 O O 1.0- 400 400 0.8- 300 - 300 DO 0.6 O 200 200 0.4- 100 100 0.2. O 0.0- 0.0 0.4 0.8 0.0 0.4 0.8 0.0 0.4 0.8 x1i x2i x1i 12 O 3.0- O 10 2.0- Standardized Residuals Square Root(|Standardized Residuals!) 2 O -2 0.0- 0 20 60 0 20 60 Fitted Values Fitted Values Figure 4.1 Plots associated with model (4.6)Sheather2009_Book AModernApproachToRegressionWit.pdf - Adobe Acrobat Pro DC (32-bit) File Edit View E-Sign Window Help Home Tools Sheather2009_Book.. x hw_4.pdf Subscribe 134 (135 of 398) A m + 125% . " for the i = 1, ... 1922 subdivisions. The first model considered was 21 90 Y, = Bot Bix ,i + B2x 2i te (4.6) Model (4.6) was fit used weighted least squares with weights, w = n where n. = the number of homes sold in subdivision i in 2006. Output from model (4.6), in the form of plots, appears in Figure 4.1. (a) Explain it is necessary to use weighted least squares to fit model (4.6) and why w, = n, is the appropriate choice for the weights. (b) Explain why (4.6) is not a valid regression model. (c) Describe what steps you would take to obtain a valid regression model (Figure 4.1). O Type here to search 15.C Sunny ~ ENG 09-03-2022 16:35 20