Please save my life… please help me…..
Question.
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:
CTract: identifying code for the census tract
P_Hsgrad: the proportion of adults who graduated from high
school
P_trades: the proportion of adults with qualifications in a
trade
P_collcert: the proportion of adults with a college
certificate
P_univdipl: the proportion of adults with a university
diploma
P_univdegr: the proportion of adults with a university degree
Popn: the number of adults with employment income
MedInc: the median employment income for persons above 15
years
AvgInc: the average employment income for persons above 15
years
StdErr: the estimated standard error of the AvgInc estimate
MedInc_4: the median employment income, with missing values
The data are in the files Assign4 – Q2.mtw and
Assign4.xls.
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?
Excel data below..
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.
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