Evaluating Michigan Schools MME Results with Regression Analysis

In my last post, I looked at factors impacting Michigan primary school test performance.   In this post I look at high school performance using the Michigan Merit Examination (MME)  11th grade  results to determine what is the  role of race, location, poverty, and school type (public, not for profit, and for profit charter).   In all of the exam subjects (Math, Reading, Science, Social Studies, and Writing) for profit charters out perform not for profit charters and public schools at a 95%, or higher, confidence level.  Not for profit charter schools typically outperform public schools at lower confidence level than their for profit comparisons because their are so few in the data (only 16 as opposed to 79).  The higher the ratio of Asian and female students, the better the school performs on the exams.

One of the advantages of a regression analysis is that it can be used to forecast what the result should be based on the factors involved.   Some schools will vary more (above and below) the forecast.  I hope to illuminate that distinction using an online map in a future post.

If you are unfamiliar with interpreting the results of regression analysis, or would like a refresher, I suggest reading this description of interpreting the results from R.

 

 Math

Coefficient Std Error t value Pr(>[t])
Intercept 1074.82 3.69942 290.536 2E−16 ***
Total Students in School 0.00805 0.00087 9.241 2E−16 ***
Ratio of Asian Students 67.5308 13.1672 5.129 3.7E−07 ***
Ratio of Black Students −14.631 2.03899 −7.176 1.6E−12 ***
Ratio of Female Students 43.3608 4.97397 8.718 2E−16 ***
localeCity: Midsize 3.46781 2.4644 1.407 0.15976
localeCity: Small 1.29456 2.24008 0.578 0.56349
localeRural: Distant 8.13805 2.47747 3.285 0.00106 **
localeRural: Fringe 7.40043 2.37748 3.113 0.00192 **
localeRural: Remote 11.5162 2.65578 4.336 1.6E−05 ***
localeSuburb: Large 1.24906 2.03834 0.613 0.54019
localeSuburb: Midsize 1.16689 2.85876 0.408 0.68325
localeSuburb: Small 6.93349 3.18744 2.175 0.0299 *
localeTown: Distant 5.04059 2.68571 1.877 0.0609 .
localeTown: Fringe 5.30112 3.07534 1.724 0.08514 .
localeTown: Remote 7.98901 2.82931 2.824 0.00486 **
Free Lunch Ratio −37.53 2.23368 −16.802 2E−16 ***
Reduced Price Lunch Ratio 18.1069 7.6958 2.353 0.01887 *
For Profit Charter 3.73045 1.33953 2.785 0.00548 **
Not for Profit Charter 4.99213 2.6868 1.858 0.06353 .
Ratio of Students Taking Math Portion 0.64986 0.12953 5.017 6.4E−07 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 10.39 on 807 degrees of freedom
Multiple R-squared: 0.7087, Adjusted R-squared: 0.7014
F-statistic: 98.15 on 20 and 807 DF, p-value: < 2.2e-16

 

Reading

Coefficient Std Error t value Pr(>[t])
(Intercept) 1091.52 3.20417 340.657 2E−16 ***
Total Students in School 0.00593 0.00075 7.856 1.3E−14 ***
Ratio of Asian Students 44.6969 11.4033 3.92 9.6E−05 ***
Ratio of Black Students −5.1164 1.76593 −2.897 0.00387 **
Ratio of Female Students 37.4981 4.30775 8.705 2E−16 ***
localeCity: Midsize 4.74126 2.13437 2.221 0.0266 *
localeCity: Small 1.74977 1.94006 0.902 0.36737
localeRural: Distant 7.69527 2.14576 3.586 0.00036 ***
localeRural: Fringe 6.17474 2.05915 2.999 0.0028 **
localeRural: Remote 9.85671 2.30019 4.285 2.1E−05 ***
localeSuburb: Large 1.72256 1.76537 0.976 0.32948
localeSuburb: Midsize 1.32051 2.47598 0.533 0.59395
localeSuburb: Small 7.20282 2.76059 2.609 0.00924 **
localeTown: Distant 4.81191 2.32606 2.069 0.03889 *
localeTown: Fringe 5.49528 2.66351 2.063 0.03941 *
localeTown: Remote 7.86533 2.45045 3.21 0.00138 **
Ratio of Free Lunch −38.487 1.93443 −19.896 2E−16 ***
Ratio of Reduced Price Lunch 17.2279 6.66521 2.585 0.00992 **
For Profit Charter 4.34289 1.16013 3.743 0.00019 ***
Not For Profit Charter 3.89918 2.32697 1.676 0.09419 .
Ratio of Students Taking Reading MME 0.54181 0.11215 4.831 1.6E−06 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.994 on 807 degrees of freedom
Multiple R-squared: 0.6857, Adjusted R-squared: 0.6779
F-statistic: 88.02 on 20 and 807 DF, p-value: < 2.2e-16

 

 Science

Coefficient Std Error t value Pr(>[t])
(Intercept) 1073.08 4.39599 244.104 2E−16 ***
# of Students in School 0.01072 0.00103 10.388 2E−16 ***
Ratio of Asian 59.5347 15.6437 3.806 0.00015 ***
Ratio of Black −12.563 2.54243 −4.941 9.4E−07 ***
Ratio of Hispanic 4.65207 5.27355 0.882 0.37796
Ratio of Females 54.1044 5.89267 9.182 2E−16 ***
localeCity: Midsize 1.32357 2.92118 0.453 0.6506
localeCity:Small 1.49458 2.65267 0.563 0.5733
localeRural: Distant 12.4171 2.96853 4.183 3.2E−05 ***
localeRural Fringe 9.46819 2.84652 3.326 0.00092 ***
localeRural: Remote 16.9671 3.20055 5.301 1.5E−07 ***
localeSuburb: Large 1.09028 2.4285 0.449 0.65359
localeSuburb: Midsize 2.74445 3.3996 0.807 0.41974
localeSuburb: Small 10.5728 3.79814 2.784 0.0055 **
localeTown: Distant 7.42551 3.19546 2.324 0.02039 *
localeTown: Fringe 7.80703 3.66525 2.13 0.03347 *
localeTown: Remote 11.0689 3.40772 3.248 0.00121 **
Free Lunch Ratio −46.743 2.7426 −17.043 2E−16 ***
Reduced Price Lunch Ratio 32.2201 9.11228 3.536 0.00043 ***
For Profit Charter 7.57878 1.58713 4.775 2.1E−06 ***
Not For Profit Charter 4.18658 3.18131 1.316 0.18855
Ratio of Science Takers 0.70856 0.1533 4.622 4.4E−06 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 12.3 on 806 degrees of freedom
Multiple R-squared: 0.7081, Adjusted R-squared: 0.7005
F-statistic: 93.12 on 21 and 806 DF, p-value: < 2.2e-16

Social Studies

Coefficient Std Error t value Pr(>[t])
(Intercept) 1111.39 2.36948 469.043 2E−16 ***
# Students in School 0.00585 0.00056 10.432 2E−16 ***
Ratio of Asians 45.281 8.42754 5.373 1.0E−07 ***
Ratio of Blacks −8.7614 1.30248 −6.727 3.3E−11 ***
Ratio of Females 25.7992 3.19851 8.066 2.6E−15 ***
localeCity: Midsize 1.5409 1.58141 0.974 0.33016
localeCity: Small 1.80375 1.43832 1.254 0.21018
localeRural: Rural 5.01472 1.58075 3.172 0.00157 **
localeRural: Fringe 4.6635 1.52854 3.051 0.00236 **
localeRural: Remote 6.68244 1.69721 3.937 8.9E−05 ***
localeSuburb: Large 0.5772 1.31018 0.441 0.65966
localeSuburb: Midsize 0.92657 1.83859 0.504 0.61443
localeSuburb: Small 3.9125 2.0505 1.908 0.05674 .
localeTown: Distant 2.99187 1.72507 1.734 0.08324 .
localeTown: Fringe 4.07701 1.97865 2.061 0.03967 *
localeTown: Remote 5.33106 1.81556 2.936 0.00342 **
Free Lunch Ratio −29.479 1.43681 −20.517 2E−16 ***
For Profit Charter 4.20834 0.8595 4.896 1.2E−06 ***
Not For Profit Charter 2.08711 1.72857 1.207 0.22763
Ratio taking Social Studies Test 0.47046 0.08312 5.66 2.1E−08 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 6.681 on 808 degrees of freedom
Multiple R-squared: 0.7403, Adjusted R-squared: 0.7341
F-statistic: 121.2 on 19 and 808 DF, p-value: < 2.2e-16

Social Studies

Coefficient Std Error t value Pr(>[t])
(Intercept) 1064.6 4.91037 216.806 2E−16 ***
# of Students in School 0.01092 0.00116 9.443 2E−16 ***
Asian Ratio 65.5835 17.4709 3.754 0.00019 ***
Black Ratio −6.689 2.70593 −2.472 0.01364 *
Female Ratio 64.0601 6.60066 9.705 2E−16 ***
localeCity: Midsize 1.63356 3.27038 0.5 0.61756
localeCity:Small −1.0047 2.97257 −0.338 0.73546
localeRural: Distant 5.65371 3.28802 1.719 0.08591 .
localeRural Fringe 2.75409 3.15531 0.873 0.38301
localeRural: Remote 9.08449 3.52459 2.577 0.01013 *
localeSuburb: Large −0.8333 2.70504 −0.308 0.75813
localeSuburb: Midsize −2.0059 3.7939 −0.529 0.59715
localeSuburb: Small 4.37433 4.23002 1.034 0.30139
localeTown: Distant 0.26317 3.56425 0.074 0.94116
localeTown: Fringe 2.42232 4.08136 0.594 0.55301
localeTown: Remote 5.82875 3.75487 1.552 0.12098
Free Lunch Ratio −48.222 2.96411 −16.269 2E−16 ***
Reduced Price Lunch Ratio 25.2679 10.2132 2.474 0.01356 *
For Profit Charter 6.61276 1.77762 3.72 0.00021 ***
Not For Profit Charter 4.79902 3.56553 1.346 0.1787
Ratio of Students Taking Social Studies Exam 0.79519 0.17161 4.634 4.2E−06 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 13.78 on 807 degrees of freedom
Multiple R-squared: 0.6286, Adjusted R-squared: 0.6194
F-statistic: 68.29 on 20 and 807 DF, p-value: < 2.2e-16

 

 

 

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