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:
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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