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Question: A policy analyst for a local school board wanted to determine whether there was a relationship be…

by | Sep 9, 2023 | Aswered Questions



A policy analyst for a local school board wanted to determine
whether there was a relationship between employment income and the
aggregate level of education. Although there were potential
problems with interpreting relationships based on aggregate data,
she decided to begin with 2011 data from census tracts in
Ottawa.

She collected and manipulated the following data for each of the
census tracts:

Question: A policy analyst for a local school board wanted to determinewhether there was a relationship be...

You should try to minimize the listing of computer output or the
excessive use of appendices in reporting your results. Summarize
the results of each regression by displaying the regression
equation, the coefficients and their standard errors.

a) Plot the average incomes and the median incomes, either
separately or together. What do these graphs suggest about the
shape of income distributions?

b) Perform a multiple regression analysis using the five
educational variables as predictor variables and the median income
(MedInc) as the response variable. Graph the
standardized residuals against the fitted values and comment on the
model assumptions.

c) The MedInc_4 variable contains the data from
the MedInc variable, but a missing value code has
been inserted for four census tracts. From the unusual observations
obtained from the “Regression Analysis” report, compare these two
variables and explain why these census tracts were selected to be
omitted from the model in (d).

The remaining questions pertain to regression models based on
the MedInc_4 variable and not the original
MedInc variable.

d) Re-estimate the multiple regression model using
MedInc_4 as the new response variable. For this
regression, save the residuals and the fitted values, calculate the
Variance Inflation Factors (click the Options button), and plot the
residuals against the fitted values.

e) What changes do you notice, comparing this model with the
previous model?

the MedInc

CTract P_HSgrad P_trades P_collcert P_univdipl P_univdegr Popn MedInc AvgInc StdErr MedInc_4
1.01 0.286285 0.065246 0.185087 0.050599 0.221039 3195 19977 25089 788 19977
1.04 0.248148 0.07037 0.155556 0.037037 0.407407 1465 30098 37886 2018 30098
1.05 0.191558 0.055195 0.209416 0.074675 0.399351 3150 34382 41786 1403 34382
1.06 0.253623 0.046377 0.201449 0.052174 0.342029 3490 35608 40529 1167 35608
1.07 0.172113 0.050109 0.159041 0.078431 0.442266 2495 36506 46688 2017 36506
1.08 0.179283 0.047809 0.201195 0.065737 0.424303 2580 38308 51257 5850 38308
2.01 0.177258 0.040134 0.210702 0.053512 0.464883 1660 36467 47772 2509 36467
2.02 0.198953 0.039267 0.180628 0.075916 0.458115 2165 28414 39677 2150 28414
2.04 0.201681 0.033613 0.117647 0.016807 0.588235 655 42961 55147 4250 42961
2.05 0.161468 0.089908 0.209174 0.056881 0.377982 2790 24152 30763 1164 24152
2.06 0.158537 0.051829 0.17378 0.070122 0.5 1780 35764 51001 2891 35764
3 0.173362 0.040169 0.150106 0.05074 0.536998 2640 29032 38211 1912 29032
4 0.237624 0.076733 0.237624 0.049505 0.30198 2060 28545 32349 1110 28545
5 0.168919 0.040541 0.168919 0.038851 0.488176 3020 31524 42434 1859 31524
6 0.173397 0.021378 0.149644 0.057007 0.555819 2230 43907 59567 2829 43907
7.01 0.142857 0.019704 0.133005 0.034483 0.615764 1195 38977 56258 3546 38977
7.02 0.271739 0.063043 0.16087 0.03913 0.258696 2340 15334 21114 826 15334
7.03 0.183463 0.02584 0.170543 0.018088 0.534884 2150 35095 55178 4092 35095
8 0.267368 0.061053 0.187368 0.033684 0.357895 2580 32682 37271 1208 32682
9 0.252941 0.061765 0.185294 0.023529 0.382353 1750 35790 40311 1643 35790
10 0.29484 0.090909 0.152334 0.054054 0.184275 1740 21974 28490 1301 21974
11.01 0.272099 0.073204 0.207182 0.035912 0.288674 3710 30061 34497 947 30061
11.03 0.15534 0.036408 0.194175 0.070388 0.507282 2535 27810 32976 1411 27810
11.04 0.176856 0.056769 0.159389 0.024017 0.4869 2215 27922 38817 1665 27922
12 0.286052 0.082742 0.179669 0.030733 0.13948 2030 22977 28075 1074 22977
13 0.221488 0.084298 0.145455 0.028099 0.34876 2755 31061 37433 1275 31061
14 0.188889 0.083333 0.172222 0.033333 0.272222 670 18226 29552 2773 18226
15 0.137584 0.031879 0.13255 0.035235 0.625839 3505 26943 45958 5000 26943
16 0.082164 0.024048 0.126253 0.042084 0.711423 2700 47666 60111 2384 47666
17 0.09292 0.022124 0.115044 0.015487 0.75 2560 46450 59723 3615 46450
18 0.074398 0.015317 0.105033 0.045952 0.743982 2425 45559 53564 2194 45559
19 0.090708 0.022124 0.117257 0.028761 0.723451 2660 37526 62781 4435 37526
20.01 0.196246 0.061433 0.177474 0.051195 0.411263 3340 20803 30634 1156 20803
20.02 0.273504 0.094017 0.15812 0.042735 0.350427 1330 23930 36899 2560 23930
21 0.255443 0.062409 0.249637 0.043541 0.269956 3515 29216 33113 895 29216
22 0.227953 0.1198 0.191348 0.051581 0.211314 2675 21605 27010 903 21605
23.01 0.24 0.041818 0.221818 0.049091 0.343636 3030 24232 34852 1818 24232
23.02 0.159204 0.024876 0.151741 0.052239 0.559701 2050 42683 48942 1664 42683
24 0.246575 0.061644 0.219178 0.027397 0.342466 1740 27992 37557 2394 27992
25 0.175847 0.050847 0.182203 0.067797 0.449153 2710 30862 48679 2902 30862
26 0.273897 0.073529 0.257353 0.040441 0.204044 2905 28959 33966 1050 28959
27 0.240566 0.058962 0.259434 0.028302 0.259434 2255 25907 30895 1035 25907
28 0.24581 0.072626 0.174581 0.03352 0.344972 3540 30577 37916 1295 30577
29 0.244094 0.070866 0.206693 0.049213 0.269685 2380 23566 29815 1146 23566
30 0.25855 0.082079 0.202462 0.043776 0.290014 3370 25706 34865 1222 25706
31 0.215649 0.083969 0.206107 0.041985 0.366412 2610 30469 45279 4104 30469
32.01 0.217125 0.012232 0.198777 0.012232 0.507645 1755 23986 37749 1934 23986
32.02 0.123878 0.019749 0.10772 0.037702 0.67684 2985 38117 53456 2161 38117
33.01 0.149194 0.046371 0.181452 0.018145 0.542339 2525 41687 49596 2343 41687
33.02 0.210031 0.062696 0.23511 0.031348 0.373041 1725 34242 39415 1581 34242
34 0.107143 0.010204 0.094388 0.033163 0.739796 2135 56978 71369 3998
35 0.179204 0.050885 0.168142 0.048673 0.462389 2295 29674 41112 2443 29674
36 0.057214 0.004975 0.072139 0.049751 0.79602 2155 43388 70296 6799 43388
37 0.125128 0.02359 0.133333 0.035897 0.636923 5250 37242 41452 935 37242
38 0.172819 0.053691 0.169463 0.068792 0.442953 2890 27979 36950 1381 27979
39 0.16568 0.035503 0.156805 0.047337 0.494083 1860 28380 36656 1920 28380
40 0.144643 0.0375 0.160714 0.042857 0.526786 2720 36058 43086 1238 36058
41 0.191095 0.055659 0.16141 0.029685 0.424861 2385 24417 32027 1065 24417
42 0.298405 0.066059 0.161731 0.031891 0.250569 1975 16747 21768 873 16747
43 0.175601 0.053604 0.184843 0.029575 0.44732 2675 30607 37163 1278 30607
44 0.105263 0.022556 0.112782 0.015038 0.736842 1515 55039 72027 11305 55039
45 0.144241 0.04521 0.156082 0.033369 0.555436 4745 43774 52503 1901 43774
46 0.191558 0.073052 0.196429 0.050325 0.340909 2785 29577 35898 1182 29577
48 0.162524 0.049713 0.143403 0.040153 0.516252 2560 38038 52651 3496 38038
49 0.09596 0.030303 0.083333 0.045455 0.709596 2095 38806 50272 2291 38806
50 0.096154 0 0.134615 0 0.673077 450 13894 27650 3869
51 0.110912 0.028623 0.137746 0.028623 0.65653 3850 20062 32339 1113
52 0.154286 0.032381 0.100952 0.024762 0.64381 3025 30969 46749 2606 30969
53 0.196581 0.039886 0.139601 0.062678 0.464387 1805 19985 32779 1610 19985
54 0.167969 0.035156 0.125 0.035156 0.59375 1395 36748 48406 4453 36748
55 0.181467 0.03861 0.158301 0.030888 0.525097 1335 39166 43547 1738 39166
56 0.156627 0.072289 0.13494 0.053012 0.436145 2055 29683 37365 1505 29683
57 0.073446 0.016949 0.112994 0.039548 0.706215 880 41251 48348 2810 41251
58 0.068127 0.021898 0.148418 0.03163 0.710462 2240 48286 63755 3152 48286
59 0.145679 0.044444 0.192593 0.022222 0.503704 2065 41738 52340 2571 41738
60 0.274892 0.071429 0.168831 0.04329 0.316017 2130 27360 34460 1471 27360
61 0.254113 0.085923 0.197441 0.025594 0.195612 2725 28148 31778 999 28148
62.01 0.2048 0.072 0.2064 0.0496 0.3712 3165 33988 40513 1412 33988
62.02 0.240343 0.103004 0.158798 0.04721 0.313305 1180 33664 38120 1863 33664
100 0.230352 0.102981 0.222222 0.03523 0.184282 1705 22917 25381 1083 22917
101 0.218845 0.066869 0.209726 0.024316 0.306991 1535 29993 35536 1461 29993
102 0.267218 0.07989 0.176309 0.041322 0.165289 1750 30275 34052 1459 30275
103 0.267057 0.097466 0.204678 0.037037 0.202729 2260 29291 33602 1101 29291
104 0.243506 0.074675 0.172078 0.058442 0.256494 1490 24978 28721 1265 24978
110 0.027778 0 0.066667 0.066667 0.838889 1065 53678 135646 16383 53678
120.01 0.065217 0.014493 0.115942 0.050725 0.724638 745 55761 112884 21879 55761
120.02 0.241627 0.059809 0.217703 0.055024 0.363636 2340 35648 41375 1488 35648
120.03 0.190299 0.050373 0.19403 0.029851 0.501866 2865 32453 43282 1746 32453
121.01 0.254673 0.067757 0.235981 0.070093 0.271028 2260 29079 35460 1411 29079
121.02 0.27566 0.064516 0.202346 0.061584 0.252199 1825 29552 38099 4811 29552
122.01 0.266289 0.076487 0.21813 0.048159 0.226629 1650 19809 24830 1080 19809
122.02 0.279895 0.086728 0.25887 0.063075 0.207622 4135 29702 34910 977 29702
122.03 0.218247 0.09839 0.200358 0.044723 0.320215 2860 33719 40908 1559 33719
123.01 0.257353 0.066176 0.216912 0.025735 0.316176 2870 27937 36520 1445 27937
123.02 0.24938 0.081886 0.208437 0.052109 0.331266 4355 35385 41207 1206 35385
124.01 0.274611 0.101036 0.227979 0.018135 0.282383 2045 32296 37107 1513 32296
124.02 0.250522 0.079332 0.237996 0.050104 0.340292 2620 35339 40457 1510 35339
124.03 0.205479 0.047945 0.22089 0.05137 0.440068 3345 43462 49107 1854 43462
124.04 0.23743 0.041899 0.268156 0.055866 0.310056 2050 34787 38920 1470 34787
125.01 0.152918 0.040241 0.205231 0.046278 0.484909 2875 31896 40904 1563 31896
125.02 0.28392 0.080402 0.266332 0.025126 0.198492 2080 34874 36640 1188 34874
125.03 0.372881 0.067797 0.118644 0.033898 0.220339 315 26901 34078 3564 26901
125.04 0.130977 0.04158 0.195426 0.04158 0.561331 2770 46034 56112 2543 46034
125.05 0.22082 0.072555 0.233438 0.055205 0.35489 3380 40813 47027 1561 40813
125.06 0.200647 0.048544 0.177994 0.072816 0.430421 3205 46855 52903 1688 46855
125.07 0.207243 0.050302 0.215292 0.05835 0.416499 2795 34195 49034 2366 34195
125.08 0.281198 0.094842 0.214642 0.066556 0.279534 3390 38509 44498 2033 38509
125.09 0.215278 0.064815 0.210648 0.106481 0.347222 2420 34306 41757 1811 34306
126.02 0.159228 0.031363 0.249698 0.038601 0.492159 4295 50689 56331 1391 50689
126.03 0.211538 0.128205 0.237179 0.032051 0.326923 770 45500 45554 2764 45500
126.04 0.278281 0.070136 0.239819 0.031674 0.230769 2270 33641 43637 3014 33641
127 0.321519 0.073418 0.24557 0.037975 0.220253 2125 35015 39300 2039 35015
130.01 0.162921 0.058989 0.205056 0.064607 0.457865 2030 39031 54431 2593 39031
130.02 0.241313 0.057915 0.266409 0.044402 0.341699 2830 31615 36625 1141 31615
131.01 0.247059 0.047059 0.239216 0.043137 0.327451 2830 28609 34164 1378 28609
131.02 0.189243 0.069721 0.213147 0.051793 0.376494 2865 26786 36348 1496 26786
132 0.196581 0.047863 0.234188 0.061538 0.369231 3255 26198 33946 1143 26198
133 0.247807 0.063596 0.219298 0.046053 0.357456 2790 30131 39193 1686 30131
134 0.256 0.093333 0.237333 0.050667 0.218667 2015 28979 33993 1326 28979
135.01 0.202128 0.047872 0.203457 0.055851 0.413564 4290 27172 39276 1423 27172
135.02 0.15704 0.066787 0.194946 0.048736 0.505415 2950 36124 49112 2081 36124
135.03 0.219895 0.062827 0.335079 0.057592 0.230366 970 32834 36846 2131 32834
136.01 0.24622 0.077754 0.257019 0.058315 0.276458 2650 32260 40214 1430 32260
136.02 0.234676 0.073555 0.262697 0.052539 0.278459 2885 29658 36703 1116 29658
137.02 0.187311 0.057402 0.250755 0.05136 0.404834 1745 33106 38051 1413 33106
137.03 0.076923 0.011834 0.171598 0.035503 0.686391 955 46510 67580 5850 46510
137.04 0.144144 0.027027 0.238739 0.031532 0.527027 1330 33428 45547 2567 33428
137.05 0.124011 0.022427 0.143799 0.05409 0.610818 4090 39810 55546 2076 39810
138 0.231959 0.061856 0.171392 0.041237 0.391753 3775 20035 29408 1099 20035
139 0.131765 0.058824 0.237647 0.035294 0.489412 2290 38093 53369 3710 38093
140.03 0.256798 0.060423 0.205438 0.066465 0.329305 1820 34467 42239 1872 34467
140.04 0.188198 0.036683 0.285486 0.047847 0.408293 3720 41170 54000 2441 41170
140.05 0.270175 0.057895 0.289474 0.035088 0.289474 3175 35537 41530 1153 35537
140.06 0.247104 0.027027 0.305019 0.050193 0.351351 1490 36244 44733 2087 36244
140.07 0.272242 0.060498 0.263345 0.051601 0.30427 3080 34721 38366 1202 34721
141.03 0.201646 0.074074 0.209877 0.041152 0.407407 1300 40454 68148 5870 40454
141.04 0.150442 0.029499 0.215339 0.035398 0.530973 1710 56133 66283 3237
141.05 0.179894 0.063492 0.285714 0.056878 0.349206 3985 39037 42199 1014 39037
141.06 0.179245 0.034591 0.176101 0.04717 0.515723 1650 38162 42606 1750 38162
141.07 0.157789 0.044221 0.21809 0.047236 0.486432 5080 44553 46646 994 44553
141.08 0.161123 0.047817 0.239085 0.056133 0.462578 4910 48558 53304 1419 48558
141.09 0.134354 0.030612 0.244898 0.057823 0.488095 3075 43181 46098 1197 43181
151.01 0.235581 0.102356 0.282697 0.039805 0.288383 6490 41159<

  

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