Question

In: Statistics and Probability

The file Stat8_prob3.txt contains data of 100 Tarrant County houses (in 1900) on variables such as value (VALUE)

The file Stat8_prob3.txt contains data of 100 Tarrant County houses (in 1900) on variables such as value (VALUE), size in square feet (SIZE), a physical condition index (CONDITION), and a depreciation factor (DEPRECIATION).

(a) Fit the model to predict VALUE using SIZE, CONDITION, and DEPRECIATION as the predictor variables.

(b) Plot the residuals e against the fitted values y^i. What departures from the regression model assumptions can you see?

(c) If any of the assumptions in part (b) have been violated, suggest a possible transformation. (Hint: Apply the Box-Cox transformation.)

(d) Fit the new model and report the new fitted regression line.

(e) Calculate the new residuals and fitted values and use the appropriate plot(s) to comment on whether the assumption of part (b) is now satisfied.

Here is the data Stat8_prob3.txt:

"VALUE","SIZE","DEPRECIATION","CONDITION"
23974,1442,.4,0
24087,1426,.4,0
16781,1632,.5,0
29061,910,.5,.18
37982,972,.55,.18
29433,912,.55,.18
33624,1400,.45,.05
27032,1087,.45,.18
28653,1139,.45,.18
33075,1386,.55,.05
17474,756,.5,.05
33852,1044,.5,.07
29046,1032,.5,0
20715,720,.55,0
19461,734,.5,0
21377,720,.5,0
52881,1635,.6,.02
43889,1381,.55,.02
45134,1372,.55,.02
47655,1349,.6,.02
53088,1599,.6,.02
38923,1171,.5,.02
57870,1966,.55,.02
30489,1504,.45,0
29207,1296,.35,0
44919,1356,.55,.12
48090,1553,.55,.1
40521,1142,.55,.1
43403,1268,.55,.1
38112,1008,.55,.1
27710,1120,.5,0
27621,960,.6,0
22258,920,.35,0
29064,1259,.5,0
12001,783,.4,0
37650,1874,.35,.02
27930,1242,.5,0
16066,772,.4,0
20411,908,.45,0
23672,1155,.45,0
24215,1004,.5,0
22020,958,.45,0
52863,1828,.6,.02
41822,1146,.6,.02
45104,1368,.6,.02
28154,1392,.65,.24
20943,1058,.65,.24
17851,1375,.55,.26
16616,648,.4,.06
38752,1313,.5,0
44377,1780,.55,0
43566,1148,.55,.32
38950,1363,.55,.32
44633,1262,.55,.32
12372,840,.35,0
12148,840,.4,0
19852,839,.5,0
20012,852,.55,0
20314,852,.55,0
22814,974,.55,0
24696,1135,.5,0
23443,1170,.7,.02
35904,960,.5,0
21799,1052,.5,0
28212,1296,.55,0
27553,1282,.55,0
15826,916,.35,0
18660,864,.5,0
21536,1404,.4,0
24147,1676,.4,0
17867,1131,.4,0
21583,1397,.4,0
15482,888,.4,0
24857,1448,.45,0
17716,1022,.45,0
224182,2251,.75,.04
182012,1126,.55,.04
201597,2617,.9,.03
49683,966,.6,.05
60647,1469,.65,.05
49024,1322,.7,.02
52092,1509,.65,.02
55645,1724,.65,.04
51919,1559,.65,.02
55174,2133,.55,0
48760,1233,.55,0
45906,1323,.55,0
52013,1733,.55,0
56612,1357,.6,0
69197,1234,.6,.17
84416,1434,.6,.15
60962,1384,.55,.17
47359,995,.55,.05
56302,1372,.65,.14
88285,1774,.7,.06
91862,1903,.7,.08
242690,3581,.8,.07
296251,4343,.8,.04
107132,1861,.75,.08
77797,1542,.65,.3

Expert Solution

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orchestra answered 2 years ago

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