state_analysis
Rogerio Luiz
2025-01-20
- Taking student data at the state level, first calculating the average gains (difference between 9th and 5th grade math scores) and 5th grade math scores separately for each cohort, then taking the mean of these cohort averages to get a single value per state.
This gives us final state-Level metrics that represent the typical performance across all cohorts.
Then, scatter plot with regression line showing relationship between initial scores (x-axis) and gains (y-axis), with residuals indicating which state over/under-performed versus predictions.
Results
black_top_ses
Math
## Correlation between 5th Grade and Dropout Rate: -0.47## Correlation between Gain and Dropout Rate: 0.46## R2 Without drop out 0.4756675## R2 with drop out 0.4996888## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_math_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.7797 -3.7241 -0.4391 3.7562 8.0028
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 118.5694 20.8585 5.684 8.69e-06 ***
## avg_state_math_5th -0.3646 0.1001 -3.643 0.00136 **
## avg_drop_out_rate 17.1778 16.3466 1.051 0.30424
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.808 on 23 degrees of freedom
## Multiple R-squared: 0.4997, Adjusted R-squared: 0.4562
## F-statistic: 11.49 on 2 and 23 DF, p-value: 0.0003477## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_math_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 58.0 194. 0.241 52.0
## 2 AM 52.8 185. 0.220 54.8
## 3 AP 54.4 170. 0.304 61.8
## 4 BA 52.7 182. 0.251 56.6
## 5 CE 53.2 203. 0.137 46.9
## 6 DF 35.9 213. 0.158 43.7
## 7 ES 53.1 199. 0.232 49.8
## 8 GO 54.0 197. 0.139 49.2
## 9 MA 63.6 175. 0.232 58.6
## 10 MG 46.0 210. 0.165 44.8
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>Reading
## Correlation between 5th Grade and Dropout Rate: -0.4## Correlation between Gain and Dropout Rate: 0.49## R2 Without drop out 0.1190966## R2 with drop out 0.2664999## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_leitura_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.936 -2.861 -1.377 3.149 22.066
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 78.0296 26.8320 2.908 0.00792 **
## avg_state_leitura_5th -0.1283 0.1427 -0.899 0.37793
## avg_drop_out_rate 45.5938 21.2074 2.150 0.04231 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.453 on 23 degrees of freedom
## Multiple R-squared: 0.2665, Adjusted R-squared: 0.2027
## F-statistic: 4.178 on 2 and 23 DF, p-value: 0.02832## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_leitura_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 69.0 181. 0.241 65.9
## 2 AM 69.5 168. 0.220 66.5
## 3 AP 66.5 155. 0.304 72.0
## 4 BA 64.0 168. 0.251 67.9
## 5 CE 62.8 193. 0.137 59.5
## 6 DF 49.5 194. 0.158 60.4
## 7 ES 66.0 181. 0.232 65.3
## 8 GO 67.8 179. 0.139 61.4
## 9 MA 66.9 162. 0.232 67.8
## 10 MG 60.3 189. 0.165 61.3
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>black_bottom_ses
Math
## Correlation between 5th Grade and Dropout Rate: -0.74## Correlation between Gain and Dropout Rate: 0.49## R2 Without drop out 0.3000958## R2 with drop out 0.3158019## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_math_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -16.091 -3.003 1.904 2.876 8.053
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 98.3857 33.8426 2.907 0.00773 **
## avg_state_math_5th -0.2690 0.1637 -1.643 0.11337
## avg_drop_out_rate 14.1737 19.0957 0.742 0.46514
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.589 on 24 degrees of freedom
## Multiple R-squared: 0.3158, Adjusted R-squared: 0.2588
## F-statistic: 5.539 on 2 and 24 DF, p-value: 0.01052## # A tibble: 27 × 6
## Uf avg_state_gain avg_state_math_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 55.6 181. 0.285 53.7
## 2 AL 60.0 166. 0.404 59.5
## 3 AM 46.4 184. 0.356 54.0
## 4 AP 51.9 169. 0.372 58.1
## 5 BA 52.6 176. 0.333 55.6
## 6 CE 61.3 180. 0.241 53.3
## 7 ES 54.4 193. 0.270 50.2
## 8 GO 55.0 191. 0.179 49.7
## 9 MA 53.6 166. 0.341 58.6
## 10 MG 49.6 199. 0.204 47.8
## # ℹ 17 more rows
## # ℹ 1 more variable: residuals <dbl>Reading
## Correlation between 5th Grade and Dropout Rate: -0.69## Correlation between Gain and Dropout Rate: 0.52## R2 Without drop out 0.1907272## R2 with drop out 0.2832186## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_leitura_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.9277 -2.2789 -0.1677 2.6976 8.0947
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 73.19874 26.73840 2.738 0.0115 *
## avg_state_leitura_5th -0.08928 0.14614 -0.611 0.5470
## avg_drop_out_rate 24.50087 13.92255 1.760 0.0912 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.362 on 24 degrees of freedom
## Multiple R-squared: 0.2832, Adjusted R-squared: 0.2235
## F-statistic: 4.742 on 2 and 24 DF, p-value: 0.01839## # A tibble: 27 × 6
## Uf avg_state_gain avg_state_leitura_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 62.9 168. 0.285 65.1
## 2 AL 69.6 150. 0.404 69.7
## 3 AM 61.1 164. 0.356 67.2
## 4 AP 62.7 154. 0.372 68.5
## 5 BA 65.3 160. 0.333 67.1
## 6 CE 72.0 165. 0.241 64.4
## 7 ES 68.9 172. 0.270 64.4
## 8 GO 65.9 173. 0.179 62.1
## 9 MA 67.5 150. 0.341 68.1
## 10 MG 63.0 179. 0.204 62.2
## # ℹ 17 more rows
## # ℹ 1 more variable: residuals <dbl>white_top_ses
Math
## Correlation between 5th Grade and Dropout Rate: -0.54## Correlation between Gain and Dropout Rate: 0.38## R2 Without drop out 0.5942884## R2 with drop out 0.5964551## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_math_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.5810 -4.7036 -0.4465 3.3702 21.6183
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 146.15913 20.97747 6.967 4.22e-07 ***
## avg_state_math_5th -0.45612 0.08961 -5.090 3.73e-05 ***
## avg_drop_out_rate -8.39365 23.88546 -0.351 0.728
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.055 on 23 degrees of freedom
## Multiple R-squared: 0.5965, Adjusted R-squared: 0.5614
## F-statistic: 17 on 2 and 23 DF, p-value: 2.936e-05## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_math_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 57.1 202. 0.222 52.1
## 2 AM 50.1 195. 0.197 55.5
## 3 AP 53.8 171. 0.302 65.4
## 4 BA 54.5 187. 0.235 58.9
## 5 CE 55.8 216. 0.0949 46.8
## 6 DF 37.2 223. 0.158 42.9
## 7 ES 51.0 220. 0.232 43.7
## 8 GO 50.9 210. 0.132 49.1
## 9 MA 57.3 184. 0.197 60.5
## 10 MG 42.1 233. 0.162 38.4
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>Reading
## Correlation between 5th Grade and Dropout Rate: -0.52## Correlation between Gain and Dropout Rate: 0.29## R2 Without drop out 0.5113434## R2 with drop out 0.5209891## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_leitura_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -13.4470 -3.8158 0.2201 1.9868 15.8392
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 153.04449 20.71003 7.390 1.63e-07 ***
## avg_state_leitura_5th -0.45149 0.09846 -4.586 0.000131 ***
## avg_drop_out_rate -14.67337 21.56122 -0.681 0.502954
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.459 on 23 degrees of freedom
## Multiple R-squared: 0.521, Adjusted R-squared: 0.4793
## F-statistic: 12.51 on 2 and 23 DF, p-value: 0.0002108## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_leitura_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 69.9 188. 0.222 64.8
## 2 AM 70.1 180. 0.197 68.9
## 3 AP 69.8 161. 0.302 76.0
## 4 BA 68.6 172. 0.235 71.9
## 5 CE 75.1 202. 0.0949 60.3
## 6 DF 50.7 205. 0.158 58.0
## 7 ES 61.5 200. 0.232 59.4
## 8 GO 65.8 193. 0.132 64.2
## 9 MA 72.6 171. 0.197 72.7
## 10 MG 57.4 210. 0.162 56.0
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>white_bottom_ses
Math
## Correlation between 5th Grade and Dropout Rate: -0.66## Correlation between Gain and Dropout Rate: 0.49## R2 Without drop out 0.4377618## R2 with drop out 0.4440434## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_math_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.2643 -2.6634 -0.0973 3.7654 8.2769
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 89.55785 16.48836 5.432 1.61e-05 ***
## avg_state_math_5th -0.21318 0.07417 -2.874 0.00857 **
## avg_drop_out_rate 5.85401 11.48345 0.510 0.61506
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.348 on 23 degrees of freedom
## Multiple R-squared: 0.444, Adjusted R-squared: 0.3957
## F-statistic: 9.185 on 2 and 23 DF, p-value: 0.001169## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_math_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 52.1 184. 0.297 52.0
## 2 AL 56.7 171. 0.410 55.5
## 3 AM 45.8 188. 0.355 51.7
## 4 AP 45.5 174. 0.385 54.7
## 5 BA 51.4 180. 0.334 53.1
## 6 CE 58.7 190. 0.242 50.4
## 7 ES 50.2 212. 0.263 45.9
## 8 GO 53.9 202. 0.162 47.4
## 9 MA 52.5 169. 0.344 55.5
## 10 MG 44.5 216. 0.201 44.6
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>Reading
## Correlation between 5th Grade and Dropout Rate: -0.69## Correlation between Gain and Dropout Rate: 0.63## R2 Without drop out 0.3386471## R2 with drop out 0.4425327## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_leitura_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7.3151 -1.9717 -0.3905 1.3437 8.5151
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 75.94963 15.57545 4.876 6.34e-05 ***
## avg_state_leitura_5th -0.09977 0.07810 -1.278 0.2142
## avg_drop_out_rate 20.47556 9.89018 2.070 0.0498 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.595 on 23 degrees of freedom
## Multiple R-squared: 0.4425, Adjusted R-squared: 0.3941
## F-statistic: 9.129 on 2 and 23 DF, p-value: 0.001206## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_leitura_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 63.6 171. 0.297 65.0
## 2 AL 69.6 155. 0.410 68.9
## 3 AM 64.2 170. 0.355 66.3
## 4 AP 60.6 159. 0.385 68.0
## 5 BA 65.0 164. 0.334 66.5
## 6 CE 71.9 176. 0.242 63.4
## 7 ES 63.8 190. 0.263 62.4
## 8 GO 67.7 184. 0.162 60.9
## 9 MA 66.7 155. 0.344 67.6
## 10 MG 60.5 194. 0.201 60.7
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>black_brown_top_ses
Math
## Correlation between 5th Grade and Dropout Rate: -0.55## Correlation between Gain and Dropout Rate: 0.55## R2 Without drop out 0.497894## R2 with drop out 0.5354845## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_math_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.597 -3.627 1.481 3.270 11.057
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 107.39275 21.00817 5.112 3.54e-05 ***
## avg_state_math_5th -0.32052 0.09446 -3.393 0.0025 **
## avg_drop_out_rate 22.91661 16.79760 1.364 0.1857
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.07 on 23 degrees of freedom
## Multiple R-squared: 0.5355, Adjusted R-squared: 0.4951
## F-statistic: 13.26 on 2 and 23 DF, p-value: 0.0001481## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_math_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 50.1 205. 0.222 46.8
## 2 AM 47.0 198. 0.200 48.6
## 3 AP 46.5 178. 0.302 57.1
## 4 BA 50.9 188. 0.242 52.6
## 5 CE 40.3 224. 0.0949 37.9
## 6 DF 32.5 220. 0.158 40.4
## 7 ES 48.7 211. 0.233 45.0
## 8 GO 48.7 209. 0.131 43.5
## 9 MA 52.5 186. 0.197 52.2
## 10 MG 40.2 224. 0.162 39.2
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>Reading
## Correlation between 5th Grade and Dropout Rate: -0.53## Correlation between Gain and Dropout Rate: 0.56## R2 Without drop out 0.3834476## R2 with drop out 0.457949## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_leitura_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.4113 -2.6414 0.0139 3.0658 11.7791
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 102.6578 20.4412 5.022 4.42e-05 ***
## avg_state_leitura_5th -0.2527 0.1015 -2.491 0.0204 *
## avg_drop_out_rate 27.5465 15.4932 1.778 0.0886 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.761 on 23 degrees of freedom
## Multiple R-squared: 0.4579, Adjusted R-squared: 0.4108
## F-statistic: 9.716 on 2 and 23 DF, p-value: 0.0008739## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_leitura_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 64.0 190. 0.222 60.7
## 2 AM 64.6 184. 0.200 61.8
## 3 AP 60.9 165. 0.302 69.3
## 4 BA 63.8 174. 0.242 65.4
## 5 CE 57.4 209. 0.0949 52.3
## 6 DF 46.7 201. 0.158 56.2
## 7 ES 60.0 192. 0.233 60.5
## 8 GO 63.3 191. 0.131 58.1
## 9 MA 65.9 173. 0.197 64.3
## 10 MG 55.5 201. 0.162 56.2
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>black_brown_bottom_ses
Math
## Correlation between 5th Grade and Dropout Rate: -0.63## Correlation between Gain and Dropout Rate: 0.54## R2 Without drop out 0.3191999## R2 with drop out 0.3741141## `geom_smooth()` using formula = 'y ~ x'
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_math_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8.1837 -2.9419 0.3022 3.2059 7.9808
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 75.34155 19.35466 3.893 0.000734 ***
## avg_state_math_5th -0.16075 0.09105 -1.766 0.090747 .
## avg_drop_out_rate 15.27568 10.75330 1.421 0.168861
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.195 on 23 degrees of freedom
## Multiple R-squared: 0.3741, Adjusted R-squared: 0.3197
## F-statistic: 6.874 on 2 and 23 DF, p-value: 0.004568## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_math_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 53.2 187. 0.297 49.8
## 2 AL 56.8 172. 0.410 53.9
## 3 AM 44.1 192. 0.355 49.9
## 4 AP 45.0 175. 0.389 53.2
## 5 BA 49.8 182. 0.334 51.1
## 6 CE 56.2 192. 0.241 48.2
## 7 ES 47.5 205. 0.263 46.4
## 8 GO 48.4 202. 0.162 45.4
## 9 MA 49.6 173. 0.344 52.8
## 10 MG 42.5 212. 0.202 44.4
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>Reading
## Correlation between 5th Grade and Dropout Rate: -0.66## Correlation between Gain and Dropout Rate: 0.62## R2 Without drop out 0.249493## R2 with drop out 0.3942836
##
## Call:
## lm(formula = avg_state_gain ~ avg_state_leitura_5th + avg_drop_out_rate,
## data = state_averages)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.2918 -1.4494 -0.1022 1.9905 7.2898
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 68.33387 17.84737 3.829 0.00086 ***
## avg_state_leitura_5th -0.06905 0.09295 -0.743 0.46506
## avg_drop_out_rate 21.54537 9.18871 2.345 0.02804 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.449 on 23 degrees of freedom
## Multiple R-squared: 0.3943, Adjusted R-squared: 0.3416
## F-statistic: 7.486 on 2 and 23 DF, p-value: 0.003134## # A tibble: 26 × 6
## Uf avg_state_gain avg_state_leitura_5th avg_drop_out_rate predicted_gain
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 AC 63.7 173. 0.297 62.8
## 2 AL 68.5 156. 0.410 66.4
## 3 AM 61.4 174. 0.355 64.0
## 4 AP 59.4 159. 0.389 65.7
## 5 BA 63.2 166. 0.334 64.1
## 6 CE 68.6 177. 0.241 61.3
## 7 ES 61.6 184. 0.263 61.3
## 8 GO 61.8 184. 0.162 59.1
## 9 MA 64.0 158. 0.344 64.9
## 10 MG 58.1 190. 0.202 59.6
## # ℹ 16 more rows
## # ℹ 1 more variable: residuals <dbl>