Linear Regression Model with R Discussion

(Use R to complete this question) The city tax assessor was interested in predicting residential
home sales prices in a mid-western city as a function of various characteristics of the home and
surrounding property. Data on 522 transactions were obtained for home sales during the year
2002. There are 11 variables.
Price: sales price of residence (dollar)
Area: fished area of residence (square feet)
Bedroom: total number of bedrooms
Bathroom: total number of bathrooms
Ac: presence or absence of air conditioning: 1 if yes, 0 otherwise
Garage: number of cars that garage will hold
Pool: presence or absence of swimming pool: 1 if yes, 0 otherwise
Year: year property was originally constructed
Quality: Index for quality of construction: 1 for high, 2 for medium and 3 for low
Lost: lost size in square feet
Highway: presence or absence of adjacency to highway: 1 if yes, 0 otherwise.
Data is in realEstate.xlsx
a)Build a regression model to predict sales price (Y) on area. The analysis should include an
assessment of all assumptions for linear model. If the regression assumptions are not met,
include an appropriate remedial measures then recheck.
b) Use the final model to predict sales price for two houses that are about to come on the market:
the first has Xd=1100 finished squares and the second X=2900 finished square feet. What is the
standard error of the two predictions, respectively?
c).On the scatter plot of the data,
• First draw a confidence band of mean response prediction. That is, the upper band
connects all upper bounds in the mean response prediction and the lower band connects
all lowers bounds in the mean response prediction.
•
Then draw a confidence band of single response prediction. That is, the upper band
connects all upper bounds in the single response prediction and the lower band connects
all lowers bounds in the single response prediction.
ID
1
2
3
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26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
price
area
bedroom bathroom ac
360000
3032
4
4
340000
2058
4
2
250000
1780
4
3
205500
1638
4
2
275500
2196
4
3
248000
1966
4
3
229900
2216
3
2
150000
1597
2
1
195000
1622
3
2
160000
1976
3
3
190000
2812
7
5
559000
2791
3
4
535000
3381
5
4
525000
3459
5
4
299900
2090
3
3
527000
3232
5
5
169900
1502
2
2
335250
2747
3
4
323900
2890
4
3
200000
1825
3
3
211000
1578
4
3
212000
1763
3
3
245000
2517
4
3
140400
1872
3
2
295000
3266
3
3
170900
2020
1
2
229000
2164
4
2
218500
2080
3
2
160000
2208
2
2
259000
3048
6
4
164500
1460
3
2
280000
2540
3
2
154000
2208
2
2
272000
2560
4
2
180000
2061
4
2
157500
1980
3
2
242500
3308
5
4
182000
2616
5
3
178000
1460
4
2
171900
1580
2
1
165500
1460
3
2
183500
1540
3
2
135000
1388
2
1
175000
1624
3
2
149500
1580
2
1
177500
1820
3
2
garage
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
pool
2
2
2
2
2
5
2
1
2
1
2
3
3
2
2
2
2
2
2
2
2
2
2
2
2
1
2
2
2
3
2
2
2
3
2
2
2
2
2
1
2
2
2
2
2
2
year
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1972
1976
1980
1963
1968
1972
1972
1955
1975
1918
1966
1992
1988
1978
1987
1984
1956
1993
1954
1957
1986
1959
1965
1985
1908
1956
1965
1959
1985
1960
1978
1940
1985
1977
1958
1957
1928
1955
1961
1951
1960
1992
1951
1948
1966
1960
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
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71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
155000
145000
178000
156000
159000
160000
112000
84000
155000
360000
104000
420000
355000
165000
244000
179900
253000
200000
200000
147700
188700
177000
585000
549900
675000
830000
920000
855000
585500
399000
790000
665000
725000
647000
780000
657500
578000
500000
484530
609000
635000
519000
625100
585444
399900
389900
649000
1733
1896
2038
1436
1690
1496
1668
980
2562
2304
1268
2283
2060
2087
2081
1696
2222
2110
1774
1592
1748
1985
2558
4000
3942
3889
3857
4756
3302
2629
4418
4746
3242
2464
4419
3877
3808
3376
2940
2654
2672
3386
3648
3455
3321
2817
3210
4
3
2
3
3
2
2
1
3
5
2
3
2
2
4
3
4
5
4
3
3
3
2
6
4
4
4
4
4
3
5
4
3
3
4
3
5
5
3
5
4
4
4
4
3
4
3
1
2
2
2
2
2
1
1
2
4
1
3
3
2
2
3
2
3
2
2
2
1
4
5
3
4
5
4
3
3
5
4
3
3
5
3
4
4
3
3
3
4
4
5
4
3
5
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
3
1
1
1
1
2
3
1
3
2
2
2
2
2
2
2
2
2
2
3
3
2
3
3
3
3
2
3
3
3
3
7
3
3
2
3
3
3
3
3
3
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1936
1925
1918
1920
1922
1900
1948
1951
1885
1978
1947
1997
1997
1966
1980
1978
1955
1957
1963
1957
1972
1948
1984
1979
1990
1991
1997
1990
1982
1989
1997
1996
1989
1992
1987
1992
1982
1947
1979
1997
1995
1994
1992
1995
1971
1996
1995
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
535000
640000
600000
582500
545000
480000
595000
610000
570000
479000
545000
335000
629000
505500
528750
370000
529000
490000
535000
612000
442500
500000
539000
545500
424000
325000
367000
470000
393000
530000
400000
403500
550000
380000
500000
465000
451500
336000
550000
450000
440000
515000
415000
380000
489500
478000
460000
3588
2705
2344
4264
2615
3608
2479
3251
2547
5032
4973
2582
3139
3516
2129
2936
3351
3136
3525
3917
2702
3644
3072
3233
2918
3266
2940
3430
2472
2878
2537
3858
2742
3460
3836
4453
4080
3301
3828
2973
2821
2950
2362
3092
2866
3369
3068
4
3
4
5
3
6
4
3
2
7
6
4
6
4
0
4
5
4
4
6
4
3
4
4
4
4
4
3
4
4
3
4
3
5
5
7
5
3
4
4
5
5
3
3
4
5
4
5
3
3
4
3
4
4
4
3
3
6
3
4
4
0
4
4
4
5
5
3
4
4
4
4
3
7
4
4
4
3
4
3
4
4
5
4
4
5
3
4
3
3
4
4
4
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
3
3
2
4
3
3
3
3
3
3
3
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
2
2
3
3
2
3
3
2
3
2
3
2
2
2
2
2
2
2
2
3
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1987
1994
1925
1995
1996
1981
1989
1985
1996
1989
1987
1966
1977
1979
1992
1987
1994
1989
1996
1995
1991
1984
1992
1991
1988
1985
1988
1966
1987
1992
1993
1987
1991
1972
1982
1974
1983
1977
1975
1980
1962
1969
1977
1978
1982
1981
1988
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
379900
390000
338000
675000
440000
500000
470000
317500
430000
430000
475000
389000
400000
395000
395000
296000
387500
353000
350000
437632
447500
318500
352000
295000
313500
330000
400000
325000
340000
399900
249900
389000
364500
357500
295000
274500
259000
415000
443000
249000
330000
291000
418000
320000
264000
381000
250000
2380
2225
2655
3855
2892
3832
3164
2620
3076
4022
3377
2858
3540
3045
4150
1778
2412
2668
2274
2936
2526
2449
3131
2536
3314
2230
2631
2638
2756
3262
1936
3148
2616
3630
1954
1926
2556
2282
3314
2001
2607
2840
3036
2240
1788
2620
1480
3
2
3
4
4
4
6
3
6
6
4
5
4
4
4
2
2
4
4
4
2
4
4
3
2
3
4
4
4
5
4
4
3
4
3
5
3
5
3
3
5
4
3
4
3
5
3
3
3
3
4
4
3
4
2
4
4
3
4
4
3
3
2
3
3
3
3
2
4
4
3
3
2
4
3
3
4
4
4
4
3
3
3
2
4
4
3
2
4
5
2
3
4
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
3
3
2
3
2
2
2
3
3
3
3
1
3
1
3
2
3
2
3
3
0
2
2
3
3
2
2
2
2
2
3
3
2
2
3
2
2
2
3
2
2
2
2
3
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1998
1997
1948
1996
1977
1952
1982
1925
1984
1986
1997
1989
1980
1991
1934
1991
1986
1978
1986
1980
1996
1985
1988
1987
1984
1986
1985
1978
1973
1978
1987
1969
1977
1969
1962
1986
1957
1987
1986
1981
1976
1965
1977
1974
1969
1965
1984
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
360000
369500
285400
409000
333000
362000
387500
239000
299900
335000
275000
328000
333000
397000
374800
520000
325000
295000
415000
224900
265000
299900
390000
271000
330000
350000
310000
340000
307000
304000
275900
315000
295000
251010
335000
343500
297000
281000
235000
237000
274900
229900
259000
245000
208000
421000
320000
2588
3138
2460
3566
2692
2958
3164
2058
2717
2920
2554
2805
2736
3516
3536
2138
2718
2178
3152
2611
2060
2448
4050
2414
3072
2525
2866
3246
2707
2300
1860
3636
1910
2280
3386
2324
1970
2062
2617
2612
2472
1922
1852
2239
2068
2101
2200
3
4
5
4
5
5
4
3
3
4
5
3
4
5
6
5
4
5
5
3
4
4
6
3
4
3
5
4
4
5
3
5
4
4
4
5
4
3
4
4
3
4
3
3
3
3
4
3
4
4
4
4
4
4
3
4
3
3
4
3
7
4
3
4
3
4
3
3
4
5
3
3
3
3
4
4
3
3
3
3
2
5
4
3
3
3
3
3
2
2
3
2
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
2
3
3
2
2
2
3
2
2
2
3
2
3
3
2
2
2
2
3
2
2
2
3
3
3
2
2
2
2
2
2
2
3
2
2
2
2
2
2
2
2
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1968
1969
1979
1976
1984
1987
1966
1969
1983
1987
1960
1988
1979
1996
1978
1956
1978
1958
1980
1987
1981
1979
1966
1914
1966
1983
1961
1987
1992
1961
1957
1976
1968
1956
1965
1967
1972
1977
1985
1985
1969
1957
1984
1986
1979
1956
1968
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
256000
275000
222000
249900
273500
218500
377000
220000
192900
298750
315000
315000
465900
239500
276000
226000
235000
247000
182000
180000
249000
260000
219900
295000
290000
300000
354900
261000
174500
244900
274900
214000
283000
177900
237500
202150
235000
217000
285000
217500
210000
183340
252000
237000
205000
285000
210000
1972
2007
2612
2124
2612
2548
2767
2025
1956
2460
2764
2004
2852
2096
2330
2520
2528
2030
2208
1500
2078
2442
2612
2268
2734
2228
3000
2404
1840
2107
2788
2416
2430
1584
1873
1644
2400
2094
2561
1752
1738
2068
2428
2090
1820
3219
2654
3
3
4
4
4
2
3
3
4
4
3
4
4
3
3
4
3
4
2
2
5
4
3
4
4
4
5
5
3
3
4
3
3
3
3
4
4
4
3
3
5
3
4
4
3
4
3
3
3
3
1
3
2
3
3
2
3
3
3
3
3
3
3
3
3
2
1
3
3
3
3
3
3
4
3
2
2
3
3
4
2
3
3
3
3
3
2
3
2
3
2
2
4
5
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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0
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1
2
2
2
3
2
2
3
2
2
2
3
2
2
2
2
2
2
3
2
0
2
2
2
3
2
2
3
3
2
2
2
2
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2
2
2
2
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2
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0
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0
0
0
0
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0
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0
0
0
0
0
1989
1959
1985
1974
1985
1984
1941
1989
1962
1967
1972
1967
1961
1977
1989
1978
1977
1988
1985
1938
1965
1969
1986
1972
1971
1982
1973
1973
1960
1947
1984
1984
1984
1989
1978
1976
1976
1984
1981
1976
1983
1977
1966
1969
1944
1944
1962
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
280000
207000
221000
257000
274000
262000
204400
254900
244000
213000
240000
235000
206000
237000
274000
275000
218400
156000
220000
171500
180000
204000
307000
265000
209900
173000
189000
222500
265000
264670
200750
227900
255000
208500
226900
215000
222950
239900
176000
228000
204900
258000
241850
198500
243000
187000
233000
1802
1765
2786
1794
2768
2288
2028
2620
1644
1888
2116
2313
1824
1942
2184
2578
2036
1384
1826
1681
1726
1910
2664
2116
2030
1940
1676
2120
2152
1984
1575
1798
2017
1904
1718
1776
2609
2226
1556
1764
1626
2012
2090
2192
2228
1825
2132
4
3
4
3
3
3
3
5
3
3
4
4
4
4
4
3
4
2
4
3
3
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3
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2
2
2
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2
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2
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2
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2
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0
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0
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0
0
0
0
0
0
0
1
0
0
0
0
0
0
1956
1976
1976
1960
1921
1963
1951
1966
1980
1958
1964
1972
1959
1972
1977
1965
1960
1961
1952
1957
1962
1958
1962
1976
1959
1956
1965
1959
1987
1966
1957
1978
1958
1978
1976
1980
1961
1955
1959
1985
1968
1967
1963
1963
1965
1963
1966
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
205000
205000
189000
204900
239000
193000
260000
188000
190500
230000
240000
235000
275000
205000
280000
190000
232500
259500
275000
183900
290000
217950
220000
185000
288000
197500
179975
195000
228400
194750
195000
210000
239550
242000
185000
175000
165000
185000
173194
205150
214200
182500
205000
208000
225000
170000
216000
2160
1974
1696
2132
1814
1796
2268
1719
1704
2142
1705
1752
2554
1650
2816
1919
2080
2108
2480
1746
2703
1640
2196
1701
2250
2502
1762
2016
1904
1652
2042
2019
2791
2514
1746
1930
1552
1566
1669
1814
1794
1691
1834
1984
1966
1669
2132
3
3
3
3
4
3
5
2
3
3
4
4
5
3
5
3
3
4
3
3
3
4
4
3
3
4
4
4
3
5
4
4
5
4
3
3
3
4
3
3
3
3
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5
4
3
4
2
2
3
3
3
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3
3
2
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2
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3
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3
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2
4
3
2
3
2
3
2
2
2
3
3
3
2
3
3
3
3
2
2
1
2
2
3
3
2
3
3
3
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3
1
1
1
1
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1
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1
1
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2
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0
0
0
0
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0
0
0
0
0
0
0
1
0
0
0
0
0
1983
1954
1968
1969
1979
1963
1971
1960
1984
1959
1972
1978
1966
1965
1946
1938
1968
1978
1964
1974
1963
1979
1972
1982
1949
1964
1959
1963
1976
1960
1963
1960
1946
1953
1984
1956
1959
1993
1964
1978
1976
1968
1959
1961
1962
1967
1976
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
180000
169200
213000
210000
185000
179900
196000
219900
159900
170000
169900
189500
195000
215000
171000
179900
120000
175000
232900
229900
174900
168900
229500
236000
205500
212000
205000
193000
180000
184000
144900
255000
137000
178000
296000
186500
170000
219000
188000
195250
175000
215000
197500
249900
180000
174900
189900
2007
1964
2325
2196
2061
1828
1956
1852
1795
1580
1708
1700
1742
1890
1512
1840
1060
1540
1550
2787
1528
1928
2329
1940
2114
1799
1864
1581
1652
1592
1520
1792
1464
1702
2180
1486
1364
1540
1608
1668
1944
1883
2215
1916
1508
1809
1958
4
4
4
4
3
3
4
6
1
2
3
4
1
4
2
3
2
3
4
4
2
2
3
4
5
3
3
3
3
4
3
2
2
3
3
2
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4
3
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2
2
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3
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3
3
2
2
3
3
2
1
1
2
1
2
1
1
1
2
2
2
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2
2
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1
2
1
2
2
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1
2
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1
2
2
1
2
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1
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1
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1
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1
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1959
1964
1973
1965
1956
1956
1968
1968
1980
1950
1950
1953
1961
1961
1956
1953
1947
1957
1962
1922
1982
1941
1960
1959
1966
1962
1940
1956
1959
1977
1953
1955
1957
1961
1952
1958
1942
1977
1969
1956
1951
1956
1948
1954
1959
1958
1935
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
154000
150000
189900
157000
182000
187650
175000
189900
175000
159900
184900
174900
143000
164900
173500
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148000
177000
149900
170000
142000
186900
152900
350000
130000
167900
184900
178000
111000
207000
190000
230000
165000
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226000
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155000
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132000
195000
155900
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175000
304000
190000
229100
187500
1592
1636
1800
1600
1550
1578
1644
1556
1672
1650
1676
1960
1649
1728
1586
1592
1514
1952
1550
1544
1566
1650
1392
2981
1412
2180
1704
1600
1276
1666
1760
1836
1636
1748
2556
1511
1524
1821
1596
2392
1748
1384
1628
1911
1624
1956
2012
2
2
3
3
3
3
3
3
3
2
3
2
3
3
3
2
2
4
3
2
3
3
2
5
2
4
2
3
3
4
3
3
3
3
4
4
3
4
1
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2
2
3
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4
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1
1
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1
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1
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1
2
1
2
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1
2
1
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1
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2
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1951
1950
1964
1950
1966
1958
1956
1959
1949
1957
1956
1947
1951
1950
1958
1951
1964
1963
1956
1957
1959
1961
1951
1950
1940
1948
1954
1957
1951
1954
1974
1946
1953
1957
1923
1954
1958
1956
1940
1960
1956
1949
1957
1953
1959
1984
1953
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
173000
170000
179000
162500
172000
153200
220000
174000
200000
161000
135000
190000
153800
144900
165000
186000
167000
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153500
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158000
175000
147000
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147000
146250
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199500
186000
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160000
125000
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155000
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146000
129000
145000
200000
149900
132000
1590
1687
1816
1622
1604
1592
1922
1892
1628
1644
1450
1592
1654
1388
1670
1953
2008
1650
1578
1618
1642
2008
1604
2035
1534
1624
1700
1630
1526
1672
1588
1752
1674
1980
1396
1178
1263
2377
1304
1340
1559
1412
1198
1424
1370
1584
1567
2
2
4
3
4
4
3
3
3
2
3
3
2
2
3
3
3
3
3
3
3
1
3
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3
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3
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4
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3
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1956
1941
1956
1956
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1956
1952
1955
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1956
1955
1959
1962
1950
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1956
1963
1960
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1962
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1941
1960
1962
1955
1955
1954
1978
1957
1949
1980
1950
1947
1927
1950
1959
1955
1937
1951
1952
1952
1920
1925
1947
1925
1957
1934
517
518
519
520
521
522
136900
137000
185000
133500
124000
95500
1409
1655
1944
1922
1480
1184
2
2
3
3
3
2
1
1
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1
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1951
1935
1939
1950
1953
1951
quality
style
2
2
2
2
2
2
2
2
3
3
3
1
1
1
2
2
2
2
2
2
2
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2
2
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2
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2
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3
3
3
3
3
3
3
3
lot
1
1
1
1
7
1
7
1
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1
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1
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5
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1
1
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7
1
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7
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5
1
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1
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highway
22221
22912
21345
17342
21786
18902
18639
22112
14321
32358
56639
30595
23172
35351
24025
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28958
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41992
30266
18829
24726
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24881
21385
28291
14752
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29307
9999
42428
6746
36100
20138
32519
47323
11123
27095
12417
22493
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26106
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2
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