Consider the multiple linear regression model fit to the rental price data in Problem 3.42.

Problem 3.42 

Table B.24 contains data on median family home rental price and other data for 51 US cities. Fit a linear regression model using the median home rental price as the response variable and median price per square foot and population as the predictor variables.

a. Construct a normal probability plot of the residuals. Is there any indication of a problem with the normality assumption?

b. Plot the residuals versus the predicted values. Is there any indication of model inadequacy?

c. Plot the residuals versus the regressor variables. Interpret these plots. Is there any indication of model inadequacy?

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95th Percentile Median Median Rental City Population Income Sale Price Price/sqft Price Los Angeles Long Beach - 3,976,322 258,144 554,700 387.32 3095 Anaheim, CA Chicago, IL 2,704,958 231,116 212,500 145.89 1600 Dallas-Fort Worth, TX Philadelphia, PA 2,172,042 235,120 222,800 1,567,872 174,127 121.74 1595 195,100 129.36 1500 Houston, TX 2,303,482 234,742 205,200 113.88 1600 Washington, DC 681,170 352,958 363,100 211.71 2200 Miami-Fort Lauderdale, FL 453,579 200,530 231,900 198.02 2100 Atlanta, GA 472,522 306,307 177,100 104.74 1295 Boston, MA 673,184 261,973 381,200 245.01 2595 San Francisco, CA 870,887 507,824 715,400 439.31 3200 Riverside, CA 324,722 198,549 305,100 183.18 1750 Phoenix, AZ 1,615,017 200,053 224,500 139.51 1300 Seattle, WA 704,352 334,519 365,800 221.63 2095 Minneapolis-St Paul, MN 716,049 222,240 227,700 176.47 1495 San Diego, CA 1,406,630 267,615 485,900 330.4 2550 St. Louis, MO 311,404 181,227 156,100 115.16 1000 Tampa, FL 377,165 251,897 166,600 122.62 1395 Baltimore, MD 614,664 204,678 238,400 171.13 1600 Denver, CO 693,060 276,281 334,200 232.07 1995 Pittsburgh, PA 303,625 181,433 130,000 110.17 1100 Portland, OR 639,863 247,701 321,400 198.28 1795 Charlotte, NC 842,051 236,485 185,400 114.5 1300 Sacramento, CA 495,234 195,061 336,300 211.64 1595 San Antonio, TX 1,492,510 177,060 194,600 113.58 1150 Orlando, FL 277,173 177,393 203,200 124.29 1450 Cincinnati, OH 298,800 182,181 143,500 103.98 1190 Las Vegas, NV Columbus, OH 632,912 180,963 206,300 129.71 1295 860,090 156,833 164,100 114.43 1200 San Jose, CA 1,025,350 347,618 843,400 547.45 3500 Austin, TX 947,890 292,201 Virginia Beach, VA 452,602 211,324 268,300 149.53 1450 202,200 132.08 1350 Nashville, TN 660,388 200,174 211,500 140.84 1500 Milwaukee, WI 595,047 139,553 185,000 129.93 1150 Jacksonville, FL 880,619 170,019 163,900 117.24 1250 Memphis, TN 652,717 162,902 133,300 81.38 995 Oklahoma City, OK 638,367 198,232 142,400 108.05 1150 Louisville, KY 616,261 182,454 159,600 116.49 995 Hartford, CT 123,243 135,161 206,600 147.96 1600 Richmond, VA 223,170 197,041 201,800 126.64 1240 New Orleans, LA 391,495 203,254 183,100 129.25 1320 Buffalo, NY 256,902 158,362 128,900 102.51 1200 Raleigh, NC 458,880 246,055 234,800 124.68 1399 Birmingham, AL 212,157 Salt Lake City, UT 193,744 Rochester, NY 208,880 Tucson, AZ Fresno, CA Worcester, MA New Haven, CT Albuquerque, NM 559,277 135,822 213,734 264,000 131,994 530,706 142,700 446,970 181,767 224,200 184,508 185,698 224,300 129,934 168,491 189,916 135,000 99.06 1000 180.17 1400 142,600 182,200 93.13 1200 117.22 1100 145.39 1200 156.55 1500 Omaha, NE 446,970 202,123 191900 152.71 1650 186,300 128.91 1200 151,900 126.05 1200