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