A random sample of new home sales (in dollars) for a four-bedroom house with 2.5 bathrooms and a two-car garage based on the age of the home and the region of the United States is given in Table 12.12.

a. Which is the row factor and which is the column factor?

b. How many levels are there for each factor?

c. How many replicates are in each cell?

d. Using Minitab, determine if there is a difference in the mean selling price of homes based on age and region of the country.

e. Is there an interaction between the age and the region of the country?

f. Create a main effects plot and an interaction plot and comment on whether these plots support your findings.

g. Check any relevant model assumptions and describe any violations that you see.

Table 12.12

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New Home Sales (in Thousands of Dollars) Based on Age and Region of the United States Northeast Southeast Midwest Western Less than 40 years 450,080 354,045 257,390 410,230 373,510 477,370 374,145 433,280 287,045 484,410 204,565 433,870 360,755 355,235 380,435 463,980 488,089 489,400 362,290 484,550 331,570 432,430 245,670 431,080 256,510 387,825 352,505 465,635 40-60 years 390,785 350,620 287,960 350,955 262,280 424,640 363,815 460,405 246,000 309,395 221,580 377,900 286,090 338,590 365,745 349,800 286,645 467,995 262,150 224,865 471,905 431,280 311,815 255,650 487,390 323,410 440,180 415,105 60+ years 311,955 454,300 321,560 371,155 244,820 455,985 238,560 377,270 409,700 461,815 326,615 465,835 296,580 368,535 263,170 453,800 218,885 356,010 275,850 388,180 480,440 382,455 378,700 418,620 286,075 336,320 438,410 384,560