Single Dependent Variable of Several Independent Variables Simultaneously Multiple Regression Problem Analysis Hi There,This assignment will run multiple r

Single Dependent Variable of Several Independent Variables Simultaneously Multiple Regression Problem Analysis Hi There,This assignment will run multiple regression models to investigate the effect on a single dependent variable of several independent variables simultaneously. The regression must be run using the programming language R. The assignment document is attached and is labeled “Multiple Regression Problem Set.pdf”, please disregard question #1 (only Question #2 needs to be completed).I have included an additional document provided by the instructor that applies to this assignment.P.S. I would also need to include the commands used in R to gain credit. Multiple Regression Problem Set
1. Do problem 13-12, pp. 415-416, in Wonnacott & Wonnacott (professors’ salaries).
2. Use the data set muni.csv from the prior problem set and answer the following questions:
a. Estimate the bivariate relationship between non-school municipal spending and income
by regressing the dependent variable per capita non-school spending on municipal
services (spendns_pc) on per capita income (income_pc), as in the prior problem set.
Can you interpret the coefficient on per capita income as an unbiased estimate of the
causal effect of per capita income on per capita non-school spending? Why or why not?
b. Include, as an additional explanatory variable, the unemployment rate (unemploy).
How has the coefficient on the income variable changed? Why did this happen? (Hint:
correlate per capita income and the unemployment rate.)
c. Interpret the coefficient on the unemployment rate. For two cities or towns that have
the same per capita income, how is expected non-school spending related to the
respective unemployment rates of their residents?
d. Add the poverty rate (poverty) as an additional independent variable. Now, how have
the coefficients on per capita income and the unemployment rate changed? Why did
the coefficient on the unemployment rate change?
e. Finally, add population as an additional independent variable. Can you interpret the
coefficient on per capita income as an unbiased estimate of the causal effect of per
capita income on per capita non-school spending? Why or why not?
f. Interpret the coefficients on each independent variable.
g. What is:
i. The proportion of the variance in the per capita non-school spending among
these 342 municipalities that is explained by this model?
ii. The typical magnitude of the error of the model in predicting a municipality’s
per capita non-school spending?
h. What is the expected per capita non-school spending for the following two
municipalities:
Municipality 1
Municipality 2
Per capita income ($)
40,000
20,000
Unemployment Rate (%)
2
10
Poverty Rate (%)
2
15
Population (# of persons)
5,000
100,000
i.
What is the expected per capita non-school spending for the following two
municipalities:
Municipality 1
Municipality 2
Per capita income ($thousands)
40
20
Unemployment Rate (proportion of the labor
.02
.10
force that is unemployed)
Poverty Rate (proportion of the population
.02
.15
with income below the poverty line)
Population (thousands of persons)
5
100
j.
Should the unemployment rate remain in the model in part (f), or should it be dropped?
(See the discussion in Chapter 13 of Wonnacott & Wonnacott.)
muni(1)
municipality
muni_code population income_pc poverty
ABINGTON
1
14605
23380
3.603416
unemploy asv_ro
ptlv_ro
spendns_pc
2.5
638407700
12193587
863.01184
ACTON
2
20331
41901
2.921226
1.2
1716057900
29910889
695.09186
ACUSHNET
3
10161
21753
3.8048301
3.5999999
ADAMS
4
8809
18572
10.336154
AGAW AM
5
28144
22562
5.6287994
ALFORD
40412
428553200
6038315
495.8472
243284411
4289104
745.5882
1152705954
17290589
879.54871
1
16450
24103
5.9344773
2.0999999
785208200
14039523
1043.4301
34874
17427
20.206076
1.3
963840300
18958739
550.97363
1360.4183
ANDOVER
399
5
7
8
ARLINGTON
6
2.7
4.0920715
AMESBURY
AMHERST
88859170
687770
9
31247
41133
3.8941314
2
2937428052
43033321
10
42389
34399
4.0624776
1.7
2797634550
49406226
1115.494
1061.177
ASHBURNHAM
11
5546
21659
6.3659511
3
266316200
4953481
705.6842
ASHBY
12
2845
21648
5.0691242
2.5999999
138584800
2455723
541.10559
ASHFIELD
13
1800
26483
7.6323118
1.9
107505874
1825450
817.39728
ASHLAND
14
14674
31641
2.0157158
2
999955577
16189281
795.89838
ATHOL
15
11299
16845
9.4389381
4.4000001
289211100
4323706
700.07501
ATTLEBORO
16
42068
22660
6.1514235
3
1444517000
22158891
892.25519
AUBURN
17
15901
23802
3.2793136
2.4000001
652941500
8697180
780.78607
AVON
18
4443
24410
6.5721359
2.8
215642700
2680439
1366.5448
AYER
19
7287
26400
10.818837
BARNSTABLE
20
47821
25554
8.8397903
BARRE
21
BECKET
22
2.2
277271600
3138715
989.43427
3
4175979952
53452543
920.24445
5113
20476
3.4476004
3.3
2798059
525.79688
1755
21861
4.5480714
2.5999999
194788960
2349155
951.29694
1.9
1194973960
14525368
1875.0459
548194230
10382799
BEDFORD
23
12595
39212
2.4873559
BELCHERTOW N
24
12968
21938
5.9000926
2.0999999
161737500
652.2135
BELLINGHAM
25
15314
25047
2.5124314
2.3
762727785
10540898
991.92426
BELMONT
26
24194
42485
4.4286313
1.4
2849598600
35107055
1359.7192
BERKLEY
27
5749
21652
2.5371828
2.4000001
297777877
3612046
738.73834
BERLIN
28
2380
28915
3.8736842
2.5
167263957
2540740
1402.9102
BERNARDSTON
29
2155
20959
4.3639741
2.8
89632900
1561405
544.74445
BEVERLY
30
39862
28626

5.7384663
1.8
2557447210
37057410
901.45825
BILLERICA
31
BLACKSTONE
32
BLANDFORD
33
BOLTON
BOSTON
38981
24953
3.7531519
8804
20936
3.7298963
1214
24285
3.3856318
34
4148
42542
1.815541
35
589141
23353
19.532242
BOURNE
36
18721
22092
BOXBOROUGH
37
4868
40794
2.3
2.8
3.2
2040803295
343824000
71416300
28367166
1016.939
5143607
519.46729
961263
537.34106
2
430044127
7057024
1110.2924
2.9000001
22235712600
260399450
1798.4902
7.1142454
3.2
1358476981
17388505
2.8142974
1.4
385566240
6508358
BOXFORD
38
7921
48846
1.3634642
1.4
947413400
12837452
824.87427
BOYLSTON
39
4008
32274
2.7729204
2
270932120
4576044
853.82788
BRAINTREE
BREW STER
991.3606
1040.321
40
33828
28683
3.7779865
2
2011670630
24622849
891.68994
41
10094
24638
3.7321169
2.5999999
1173174661
13984242
1174.0386
BRIDGEW ATER
42
25185
23105
3.5377247
2.3
1090160500
15294952
579.07312
BRIMFIELD
43
3339
23711
4.3793416
3
158579705
2532518
591.71783
2339278634
BROCKTON
44
BROOKFIELD
45
BROOKLINE
46
BUCKLAND
47
BURLINGTON
CAMBRIDGE
94304
14.487736
3.5999999
42247372
1035.1349
6.1472716
2.7
104507857
1806941
619.65356
57107
17163
3051
44327
9.2827682
1.2
6095445600
77838054
1494.3702
1991
20144
20033
6.8568568
1452591
551.66821
1
77928700
48
22876
30732
1.899593
1.8
1582559645
16300364
1475.9331
49
101355
31156
12.936218
1.6
6772661667
56706391
1841.5801
CANTON
50
20775
33510
3.3971739
1.9
1380886300
19622394
1076.566
CARLISLE
51
4717
59559
2.3571885
1.1
645448722
11488987
1252.3406
CARVER
52
11163
20398
5.0162106
2.9000001
454949723
7656804
734.85577
CHARLEMONT
53
1358
19577
10.442349
3.3
57490877
1154417
642.91742
CHARLTON
54
11263
23626
5.6068006
2.7
513067350
7100852
550.07587
CHATHAM
55
6625
28594
4.8449912
2.7
1620632900
16335980
2648.1021
2100207900
36417605
56
33858
2.8141127
1.8
CHELSEA
57
35080
14628
23.303226
3.9000001
568102590
7349673
1235.0933
CHESHIRE
CHELMSFORD
58
3401
19156
6.6054502
3.3
134995800
1552452
429.37051
4.9000001
CHESTER
59
CHESTERFIELD
30465
1308
18098
5.8461537
60
1201
19220
5.6856189
CHICOPEE
61
CLARKSBURG
54653
18646
12.251103
63
1686
19389
6.6032124
CLINTON
64
13435
22764
7.1466227
COHASSET
65
7261
42909
998729
691.71899
1.7
59261268
1273525
537.05157
3.3
1537806600
25604480
785.46545
785593
420.44177
3
2.7
63613328
870.09454
58321660
465156940
7498330
852.48212
921287700
13902231
1560.1707
2.7947719
1.6
COLRAIN
66
1813
18948
6.800446
2.5999999
75563588
1409261
628.02936
CONCORD
67
16993
51477
3.9255934
1.2
2425296097
29346083
1105.1229
CONW AY
68
1809
25605
3.4864416
1.9
107444723
2009216
780.25049
CUMMINGTON
69
978
21553
6.6366706
2.3
54405439
786703
485.17529
DALTON
70
6892
23634
2.7439928
2.5
264453661
4881814
524.48474
DANVERS
71
25212
26852
2.9358327
1.7
1528269077
22633665
1199.1227
DARTMOUTH
72
30666
24326
4.5359921
3.9000001
1757975824
21007811
550.36261
DEDHAM
73
23464
28199
4.5850468
2.3
1444806300
21310893
1362.2119
DEERFIELD
74
4750
24555
4.4842105
2
256699640
3850495
725.84332
DENNIS
75
15973
25428
7.0288944
4.3000002
2082696260
17994495
1197.5284
DIGHTON
76
6175
22600
2.6069849
2.9000001
302577721
4136237
518.23865
DOUGLAS
77
7045
23036
4.6296296
2.7
345537745
5870686
796.57953
DOVER
78
5558
64899
2.9724374
1
1086314483
12362259
1177.3861
DRACUT
79
28562
23750
3.6979916
2.5
1285700635
20172643
600.34979
DUDLEY
80
10036
21546
5.598999
2.9000001
360736400
4400984
392.69638
DUNSTABLE
81
2829
30608
1.9496633
2
206933160
3240573
770.97205
82
14248
2.2835259
1.6
1662032405
24664561
EAST BRIDGEW ATER
83
12974
23532
4.0786085
2.5999999
567416700
10202152
848.40985
EAST BROOKFIELD
DUXBURY
84
2097
22629
40242
3.9347408
3.5
97189546
1030209
474.37122
EAST LONGMEADOW
85

14100
27659
3.4415584
2.4000001
743750095
15194814
698.91595
EASTHAM
86
5453
24642
6.9831886
3.9000001
783807400
9178385
980.46057
1327.418
EASTHAMPTON
87
15994
21922
8.8830252
2.4000001
552367364
9401293
706.01843
EASTON
88
22299
30732
1.9563838
2.4000001
1233977900
20039801
796.13672
EGREMONT
90
1345
41702
5.1224942
1.2
183442435
1911470
870.87244
ERVING
91
1467
19107
6.7307692
2.7
54306405
192245
960.97424
ESSEX
92
3267
31613
6.5809612
2.0999999
294027700
3925270
790.89319
EVERETT
93
38037
19845
11.815867
3
1197695171
12468007
1404.8635
4.1999998
718127100
10872444
719.8988
5
2163503900
22630251
907.80225
2.7
3730651595
42753267
1091.4066
895731407
16311269
1089.4458
FAIRHAVEN
FALL RIVER
FALMOUTH
FITCHBURG
FLORIDA
FOXBOROUGH
94
16159
20986
9.0446835
95
91938
16118
17.112009
96
32660
27548
6.9475055
97
39102
17256
15.021357
4
98
676
16979
5.8055153
4.3000002
99
16246
32294
3.1230597
1.9
23701000
223974
1393.9235
939363952
14522567
855.97455
FRAMINGHAM
100
66910
27758
8.0465536
1.9
3327003842
53664572
992.05859
FRANKLIN
101
29560
27849
2.8370757
1.8
1851355400
24271269
710.09125
FREETOW N
102
8472
24237
4.9530821
GARDNER
103
20770
18624
3.5
421138700
6085454
585.21191
725.81042
3.8
28846
4.2012239
2.0999999
7071164
923.85583
1363
23381
4.4020543
1.5
60760924
925996
568.12689
107
30273
25595
8.8042316
3.8
2087429200
108
921
22221
7.871397
1.5
110
14894
105
480286300
9216694
9.6209459
7377
106
GLOUCESTER
GOSHEN
GEORGETOW N
GILL
467051800
30956575
943.2572
62491720
1031738
659.86603
26952
5.6445565
2.7
666524151
10531082
GRANBY
111
6132
23209
2.2123163
2.7
263055217
4348303
537.078
GRANVILLE
112
1521
22315
3.384207
2.5
80935235
1343525
897.93567
GRAFTON
598.13898
GREAT BARRINGTON
113
7527
22655
7.2083879
2.3
416677000
7150177
744.7674
GREENFIELD
114
18168
18830
13.970968
2.7
551485048
11956196
999.01257
GROTON
115
9547
33877
3.9549806
1.8
675923582
12714123
806.45215
GROVELAND
116
6038
25430
4.4551177
2.2
335063935
5126478
585.49969
HADLEY
117
4793
24945
6.89433
1.8
272072600
3545105
899.47583
HALIFAX
118
7500
23738
3.3257341
2.9000001
339756200
5538026
738.32098
688395900
10807816
664.85596
4743007
793.42853
HAMILTON
119
HAMPDEN
120
8315
33222
5.3422151
5171
26690
2.2138762
HANCOCK
121
721
HANOVER
122
13164
HANSON
123
HARDW ICK
124
1.4
2.3
22250
5.6944447
30268
2.3439879
9495
23727
3.8127515
2.7
2622
20824
7.494235
3.9000001
0.5
1.8
269949225
74488800
402240
301.04669
868852000
15795729
992.59235
514843900
111809953
8469182
812.70673
1710692
532.42065
HARVARD
125
5981
40867
2.0232868
1.4
574930300
7934038
1011.6074
HARW ICH
126
12386
23063
5.5412693
3.7
1529810322
17898781
1765.5924
HATFIELD
127
3249
24813
2.7734976
2.4000001
180525380
2390156
686.94562
HAVERHILL
128
58969
23280
9.0973768
3
2012503825
34715691
906.74323
HAW LEY
129
336
17333
14.199396
2.5
21380289
315145
1144.6206
HEATH
130
805
24777
9.4017096
1.9
44556215
865282
1046.8723
HINGHAM
131
19882
41703
3.4877801
1.5
2009206664
29354509
1162.5532
HINSDALE
132
1872
19797
8.2397003
4.4000001
99045972
1551060
498.99493
HOLBROOK
133
10785
23379
6.3724113
2.7
449293500
8055832
997.40948
HOLDEN
134
15621
27971
3.1009257
1.9
822766000
15040162
730.38562
HOLLAND
135
2407
21770
7.2864323
4.0999999
146527500
2460197
536.59546
HOLLISTON
136
13801
32116
3.4257038
1.7
972146643
17479197
891.93188
HOLYOKE
137
39838
15913
26.384382
4.1999998
749541362
11940194
1181.2966
HOPEDALE
138
5907
24791
4.0166206
2.0999999
296254315
5030398
1058.7722
HOPKINTON
139
13346
41469
1.6622591
1.8
1185098052
18606040
1032.1578
HUBBARDSTON
140
3909
23072
3.6874678
3.7
161629500
2652340
520.51239
HUDSON
141
18113
26679
4.4608221
2.3
903889312
12184428
895.55347
HULL
142
11050
26331
8.3325768
3.4000001
789136007
13510008
1201.6366
HUNTINGTON
143
2174
19385
5.7771664
3.5
89198332
1436093
402.13565
IPSW ICH
144
12987
32516
7.1301384
2
1036116530
14402020
882.70026
KINGSTON
145
11780
23370
5.7853379
2.3
631311500
10347195
933.52948
LAKEVILLE
146
9821
26046
2.9623449
2.8
554216500
7088429
898.41022
LANCASTER
147
7380
21010
4.1498861
2.0999999
321295900
4854781
484.48495
LANESBOROUGH
148
2990
21106
5.6856189
2.5
152759100
2306662
805.29205
LAW RENCE
149
72043
13360
24.337391
6.4000001
988212062
15475401
779.21539
LEE
150
5985
19799
6.6838045
3.0999999
265215467
3935798
811.89642
LEICESTER
151
10471
20822
4.3046026
2.8
355677967
5854459
632.34265
LENOX
152
5077
23263
8.8848038
3
367542356
4851559
1294.9481
LEOMINSTER
153
41303
21769
9.5050716
3.2
1397898350
22170668
682.86853
LEVERETT
154
1663
31891
5.38415
1.4
128487200
2379583
627.75507
LEXINGTON
155
30355
46119
3.3857844
1.2
3761567000
46079196
956.31439
4.6936116
LEYDEN
156
772
26076
LINCOLN
157
8056
49095
########
3.2
########
40276650
710077
557.40405
1121711730
12866034
1168.3818
LITTLETON
158
8184
31070
3.5855589
1.6
568046513
8003775
1009.8304
LONGMEADOW
159
15633
38949
2.0515518
2
1212331300
23131281
857.01111
3.3
160
105167
2160890020
39760376
LUDLOW
161
21209
20105
6.3545837
3.4000001
765717969
12864062
769.32721
LUNENBURG
LOW ELL
162
9401
26986
17557
4.0698915
16.782543
2.9000001
541347800
8997200
647.40802
1114.9574
LYNN
163
89050
17492
16.517508
3.4000001
2353777938
41614794
1149.3916
LYNNFIELD
164
11542
39560
2.5038989
1.5
1092901666
14404444
857.97937
MALDEN
165
56340
22004
9.165637
2.5
1709373505
29794380
1085.1162
MANCHESTER
166
5228
47910
4.7893825
1.5
953387710
10325189
1390.9529
MANSFIELD
167
22414
27441
4.4555559
2.4000001
1196740400
20332619
955.45654
MARBLEHEAD
168
20377
46738
4.272912
1.5
2468188927
27495625
1011.6411
MARION
169
5123
37265
4.6178346
2.3
627391800
7854945
1231.2018
MARLBOROUGH
170
36255
28723
6.8470225
2.2
1701236700
26126062
797.77917
MARSHFIELD
171
24324
28768
5.3874693
2.0999999
1734774524
26125704
779.19086
MASHPEE
172
12946
25215
5.4628105
3.8
1315822010
18829413
1332.6432
MATTAPOISETT
173
6268
28050
3.5702851
2.5
625485468
8919423
796.18646
MAYNARD
174
10433
27016
5.5988455
2.2
569505698
10222627
1283.8156
MEDFIELD
175
12273
42891
1.4301066
1.5
1029151250
16970704
1052.673
MEDFORD
176
55765
24707
6.3776984
2.0999999
2484078700
39546533
999.72736
MEDW AY
177
12448
27578
2.2553952
1.8
727539523
12651912
763.70618
MELROSE
178
27134
30347
3.3480144
1.9
1883278024
26422391
1033.2446
MENDON
179
5286
27693
4.0136313
2.2
331843249
4612621
710.54034
MERRIMAC
180
6138
24869
2.7053616
2.3
286379514
4470384
795.97504
METHUEN
181
43789
22305
7.3822098
3.5
1933688085
29334048
869.1048
MIDDLEBOROUGH
182
19941
20246
5.4920144
3.4000001
793358000
13502953
961.06677
MIDDLEFIELD
183
MIDDLETON
184
MILFORD
542
24137
8.6206894
7744
29031
3.6996222
185
26799
MILLBURY
186
12784
23531
6.259542
MILLIS
187
7902
27957
23742
7.2059822
504218
686.45319
1.9
1.7
510647683
7731206
984.70313
2.5
1122813360
18582561
2.5
30174625
487658100
800.87445
7636726
717.57446
911.68909
1.8
188
2724
20497
5.8014131
2.9000001
114167895
1938571
565.10596
189
26062
37138
2.7849922
1.9
2107968065
31682760
969.07343
4.1999998
MONROE
190
MONSON
191
MONTAGUE
192
MONTEREY
193
MONTGOMERY
194
NAHANT
196
93
12400
21.818182
8359
22519
5.5775905
3
13.114166
2.9000001
9.0413942
2.7
8489
17794
934
30992
654
25942
2.9366305
2.2
3632
41807
2.5763092
1.7
444173150
8070627
2.9370451
MILLVILLE
MILTON
5231096
337880250
271043281
162098374
49111000
344826890
69835
2266.4788
6162936
862.70001
4537265
598.13159
1510757
1146.8317
684607
635.16248
4451715
1268.6656
NATICK
198
32170
36358
2.7747965
1.5
2233641550
33772660
1395.9562
NEEDHAM
199
28911
44549
2.5159702
1.4
3156367492
37118882
1187.0013
NEW ASHFORD
200
247
28323
2.1551723
6.3000002
14306000
78540
502.19498
NEW BEDFORD
201
93768
15602
20.200558
6.5
2107259942
34200829
1043.0709
NEW BRAINTREE
202
927
21072
4.5701852
3
44842742
754255
515.3537
NEW MARLBOROUGH 203
1494
25658
6.405694
2
162407285
1760495
692.67224
NEW SALEM
204
929
23234
6.2975025
3.5999999
48992810
695698
636.54291
NEW BURY
205
6717
34640
3.1226542
2.0999999
538448162
7193667
839.56543
NEW BURYPORT
206
17189
34187
5.182909
2
1094579467
18399880
950.72644
NEW TON
207
83829
45708
4.3136106
1.3
9885690995
119221433
1046.7256
NORFOLK
208
10460
32454
1.0935881
2.0999999
670447600
10633299
767.69684
NORTH ADAMS
209
14681
16381
18.175943
3.3
293915299
4596835
1101.3333
NORTH ANDOVER
210
27202
34335
2.9206023
2.2
1768953014
26375089
788.13971
NORTH ATTLEBOROUGH
211
27143
25974
3.8445854
2.4000001
1155507100
17193946
853.49042
5.4513736
2.4000001
NORTH BROOKFIELD
212
4683
20205
NORTH READING
213
13837
30902
1.4865555
NORTHAMPTON
214
28978
24022
9.8214283
NORTHBOROUGH
215
14013
32889
2.7922454
NORTHBRIDGE
216
13182
22515
5.2841396
1.9
1.9
160508288
2186123
535.19336
1027535400
16584421
1068.3792
1152367703
18518549
1060.7238
1.9
897230263
15109358
745.26404
2.7
518679100
7520847
731.67255
NORTHFIELD
217
2951
21517
5.0408721
2
132772480
1919890
638.97974
NORTON
218
18036
23876
4.0096765
2.4000001
854048600
12178733
790.69977
NORW ELL
219
9765
37222
1.872189
1.3
1019572957
14824591
1121.4459
NORW OOD
220
28587
27720
4.3718376
2
1551440141
18881027
1825.4608
OAK BLUFFS
221
3713
23829
8.429841
2.9000001
738165100
8747257
2211.1199
OAKHAM
222
1673
23175
1.9196161
2.5999999
86214162
1125095
444.36182
ORANGE
223
7518
17361
7.7993312
4.0999999
184748500
3728225
736.90814
ORLEANS
224
6341
29553
6.464745
3
1178994400
9974293
1667.9373
OTIS
225
1365
25029
7.3964496
4.1999998
238173000
2162611
840.28833
OXFORD
226
13352
21828
7.777441
3
452834626
7779699
633.94214
PALMER
227
12497
18664
7.8806982
3.5
411053100
7583930
941.84235
PAXTON
228
4386
29573
1.8463074
1.8
225497100
4434418
1362.3789
PEABODY
229
48129
24827
5.3305531
2.0999999
2481076854
25579902
1161.6334
PELHAM
230
1403
29821
4.8710604
2
83321724
1699763
595.43469
PEMBROKE
231
16927
27066
4.8094049
2.2
966022101
14374409
664.3324
PE…
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