Data Preparation:

  1. State for assignment: Texas, Travis County.
  1. Data: ACS 2013-2017, Census Tract Level, IPUMS NHGIS by way of the US Census Bureau.
  2. Variables: This report seeks to examine the association between white student enrollment (DV) and the proportion of Black and Latinx residing in the tract.
  3. 2 rows were deleted due to missingness
  4. DV: The Proportion of White Student Enrollment in Tract
#Downloading neccessary libraries for project, each accompanied with functions neccessary to perfrom this project. Two datasets are imported: The first dataset represents the number of students enrolled in Census Tracts nationwide The second dataset represents the number of people living in each Census Tract by race - also nationwide. I merge these datasets together, joining them via the GISJOIN variable.

library(readxl)
library(car)
## Loading required package: carData
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:car':
## 
##     recode
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
library(pastecs)
## 
## Attaching package: 'pastecs'
## The following objects are masked from 'package:dplyr':
## 
##     first, last
cen_sch_enroll <- read_excel("~/Library/CloudStorage/iCloud Drive/Desktop/cen_sch_enroll.xlsx")
census_race_eth <- read_excel("~/Library/CloudStorage/iCloud Drive/Desktop/census_race_eth.xlsx")
project1 <- merge(cen_sch_enroll, census_race_eth, by="GISJOIN")
#The dataset provides the number of children enrolled for each grade. I sum the number of children enrolled in K-12 (from kindergarten ending in 004 to 12th grade ending in 16). I do this by race, where k_12 = total students, bk_12 = total black students, wk_12 = white students and lk_12 = latinx students. 
project1$k_12<-project1$AH0TE004+project1$AH0TE005+project1$AH0TE006+project1$AH0TE007+project1$AH0TE008+project1$AH0TE009+project1$AH0TE010+project1$AH0TE011+project1$AH0TE012+project1$AH0TE013+project1$AH0TE014+project1$AH0TE015+project1$AH0TE016

#total amount of black students enrolled in primary school in the tract
project1$bk_12<-project1$AH0VE004+project1$AH0VE005+project1$AH0VE006+project1$AH0VE007+project1$AH0VE008+project1$AH0VE009+project1$AH0VE010+project1$AH0VE011+project1$AH0VE012+project1$AH0VE013+project1$AH0VE014+project1$AH0VE015+project1$AH0VE016

#total amount of white students enrolled in primary school in the tract
project1$wk_12<-project1$AH01E004+project1$AH01E005+project1$AH01E006+project1$AH01E007+project1$AH01E008+project1$AH01E009+project1$AH01E010+project1$AH01E011+project1$AH01E012+project1$AH01E013+project1$AH01E014+project1$AH01E015+project1$AH01E016

#total amount of latinx students enrolled in primary school in the tract
project1$lk_12<-project1$AH02E004+project1$AH02E005+project1$AH02E006+project1$AH02E007+project1$AH02E008+project1$AH02E009+project1$AH02E010+project1$AH02E011+project1$AH02E012+project1$AH02E013+project1$AH02E014+project1$AH02E015+project1$AH02E016

#Changing the variable names for population (by race) in tract variables
project1$total_pop<-project1$AHZAE001
project1$latinx_pop<-project1$AHZAE012
project1$black_pop<-project1$AHZAE004
project1$white_pop<-project1$AHZAE003
#Creating a percentage (really a proportion) of racial groups within tract. 
project1$black_per_k_12<-project1$bk_12/project1$k_12
project1$white_per_k_12<-project1$wk_12/project1$k_12
project1$latinx_per_k_12<-project1$lk_12/project1$k_12
project1$black_per_pop<-project1$black_pop/project1$total_pop
project1$white_per_pop<-project1$white_pop/project1$total_pop
project1$latinx_per_pop<-project1$latinx_pop/project1$total_pop
#Subsetting the dataset to pull Travis County and exclude the rest of nation.
proj3<-subset(project1,COUNTY.x == "Travis County")

Data Analysis

This section displays descriptive statistics, quartile distributions, correlations, scatterplots and regression models pertaining to the aforementioned variables selected for this project.

As previously noted, I seek to examine the association between white student enrollment (DV) and the proportion of Black and Latinx residents living in the tract. Specifically in Travis county. I hypothesize a negative asssociation between the outcome and both predictor variables because of the current nature of gentrification and displacement in the city of Austin. Much of the city’s historically black and latinx neighborhoods are rapidly becoming white, but that gentrification is only exhibited in the communities, not the schools serving those communities. In other words, there is a possibillity that the white children living in the tract are not attending these schools. This gives me the opportunity to examine how white student enrollment relates to tracts carrying significant black and latinx populations, an alternative reflection of segregation.

First, I run descriptives:

#Descriptives
attach(proj3)
x<-cbind(black_per_k_12,latinx_per_k_12,white_per_k_12,black_per_pop,latinx_per_pop,white_per_pop)
stat.desc(x)
##              black_per_k_12 latinx_per_k_12 white_per_k_12 black_per_pop
## nbr.val        2.160000e+02    216.00000000   216.00000000  2.170000e+02
## nbr.null       7.400000e+01     10.00000000     8.00000000  7.000000e+00
## nbr.na         2.000000e+00      2.00000000     2.00000000  1.000000e+00
## min            0.000000e+00      0.00000000     0.00000000  0.000000e+00
## max            5.346260e-01      0.97905028     1.00000000  4.650048e-01
## range          5.346260e-01      0.97905028     1.00000000  4.650048e-01
## sum            1.746119e+01     96.24496664    82.38281712  1.638517e+01
## median         3.364780e-02      0.42907900     0.33445383  4.864434e-02
## mean           8.083886e-02      0.44557855     0.38140193  7.550771e-02
## SE.mean        7.490153e-03      0.01972697     0.02002380  5.598515e-03
## CI.mean.0.95   1.476353e-02      0.03888303     0.03946810  1.103471e-02
## var            1.211812e-02      0.08405715     0.08660576  6.801511e-03
## std.dev        1.100823e-01      0.28992611     0.29428857  8.247127e-02
## coef.var       1.361750e+00      0.65067341     0.77159695  1.092223e+00
##              latinx_per_pop white_per_pop
## nbr.val        217.00000000  217.00000000
## nbr.null         0.00000000    0.00000000
## nbr.na           1.00000000    1.00000000
## min              0.04510184    0.03805395
## max              0.85106033    0.94204656
## range            0.80595849    0.90399261
## sum             70.58179050  111.41492040
## median           0.27374486    0.53327186
## mean             0.32526171    0.51343281
## SE.mean          0.01448204    0.01571734
## CI.mean.0.95     0.02854422    0.03097899
## var              0.04551132    0.05360654
## std.dev          0.21333382    0.23153087
## coef.var         0.65588361    0.45094677
summary(x)
##  black_per_k_12    latinx_per_k_12  white_per_k_12   black_per_pop    
##  Min.   :0.00000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.1794   1st Qu.:0.1091   1st Qu.:0.02010  
##  Median :0.03365   Median :0.4291   Median :0.3345   Median :0.04864  
##  Mean   :0.08084   Mean   :0.4456   Mean   :0.3814   Mean   :0.07551  
##  3rd Qu.:0.12813   3rd Qu.:0.7203   3rd Qu.:0.6693   3rd Qu.:0.10305  
##  Max.   :0.53463   Max.   :0.9791   Max.   :1.0000   Max.   :0.46500  
##  NA's   :2         NA's   :2        NA's   :2        NA's   :1        
##  latinx_per_pop   white_per_pop    
##  Min.   :0.0451   Min.   :0.03805  
##  1st Qu.:0.1423   1st Qu.:0.30426  
##  Median :0.2737   Median :0.53327  
##  Mean   :0.3253   Mean   :0.51343  
##  3rd Qu.:0.4863   3rd Qu.:0.72905  
##  Max.   :0.8511   Max.   :0.94205  
##  NA's   :1        NA's   :1

The descriptives here are telling. First, we see that the median proportion of students enrolled in school is highest among latinx (.429), followed by whites (.335). The proportion of black students enrolled is fairly low among blacks. This of course can be due to the difference in the number of school aged children per race or even differences in fertility rates. Surely, tract population sizes matter. The number of residents living in the tract however is highest among whites (.533) than any other group. In pure descriptives, there are more whites living in the tract than attending schools. Again, the number of school aged children by race would be essential to examining why. It is important to note that the mean for each variable is relatively similar to the mode, sometimes falling no more than 3 tenths away from eacother. This indicates that there are few outliers that manipulate the mean’s credibiliity.

Next, I compute quartile distributions.

#Quartiles
quantile(proj3$white_per_k_12, na.rm=TRUE)
##        0%       25%       50%       75%      100% 
## 0.0000000 0.1091225 0.3344538 0.6693167 1.0000000
qqnorm(proj3$white_per_k_12,main="White School Enrollment: Source - ACS 2013-2017",pch=1,frame=FALSE)

quantile(proj3$black_per_k_12, na.rm=TRUE)
##        0%       25%       50%       75%      100% 
## 0.0000000 0.0000000 0.0336478 0.1281264 0.5346260
qqnorm(proj3$black_per_k_12,main="Black School Enrollment: Source - ACS 2013-2017",pch=1,frame=FALSE)

quantile(proj3$latinx_per_k_12, na.rm=TRUE)
##        0%       25%       50%       75%      100% 
## 0.0000000 0.1794015 0.4290790 0.7203101 0.9790503
qqnorm(proj3$latinx_per_k_12,main="Latinx School Enrollment: Source - ACS 2013-2017",pch=1,frame=FALSE)

quantile(proj3$white_per_pop, na.rm=TRUE)
##         0%        25%        50%        75%       100% 
## 0.03805395 0.30426022 0.53327186 0.72904586 0.94204656
qqnorm(proj3$white_per_pop,pch=1,main="White Tract Population: Source - ACS 2013-2017",frame=FALSE)

quantile(proj3$black_per_pop, na.rm=TRUE)
##         0%        25%        50%        75%       100% 
## 0.00000000 0.02010211 0.04864434 0.10304659 0.46500479
qqnorm(proj3$black_per_pop,pch=1,main="Black Tract Population: Source - ACS 2013-2017",frame=FALSE)

quantile(proj3$latinx_per_pop, na.rm=TRUE)
##         0%        25%        50%        75%       100% 
## 0.04510184 0.14226861 0.27374486 0.48632634 0.85106033
qqnorm(proj3$latinx_per_pop,pch=1,main="Latinx Tract Population: Source - ACS 2013-2017",frame=FALSE)

Comparing quartiles across the variables, we see the spread of data is more evenly distributed across white student enrollment and white population within in tract. This is partially true for latinx, both in enrollment and population. However, the spread of data for black student enrollment and tract population is less informative. Majority of the data for black student enrollment takes place above the mean - and because the mean is so low, this indicates that there are numerous census tracts in Travis County that do not carry black students whatsoever. So too is this similar for black population shares. I would wager that the majority of the black population in the county is situated in suburban cities, but are fairly minimal contrast to white and latinx population shares.

Now, we run correlations.

#Correlations performed between % of white student enrollment and % of black and latinx population living in tract.
cor.test(proj3$white_per_k_12, proj3$black_per_pop, method="pearson",use="complete.obs")
## 
##  Pearson's product-moment correlation
## 
## data:  proj3$white_per_k_12 and proj3$black_per_pop
## t = -9.6693, df = 214, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.6379467 -0.4511272
## sample estimates:
##        cor 
## -0.5514128
cor.test(proj3$white_per_k_12, proj3$latinx_per_pop, method="pearson",use="complete.obs")
## 
##  Pearson's product-moment correlation
## 
## data:  proj3$white_per_k_12 and proj3$latinx_per_pop
## t = -21.95, df = 214, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8690797 -0.7859383
## sample estimates:
##        cor 
## -0.8321268
cor.test(proj3$white_per_k_12, proj3$white_per_pop, method="pearson",use="complete.obs")
## 
##  Pearson's product-moment correlation
## 
## data:  proj3$white_per_k_12 and proj3$white_per_pop
## t = 29.978, df = 214, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.8695317 0.9216303
## sample estimates:
##       cor 
## 0.8987061
cor.test(proj3$white_per_k_12, proj3$black_per_k_12, method="pearson",use="complete.obs")
## 
##  Pearson's product-moment correlation
## 
## data:  proj3$white_per_k_12 and proj3$black_per_k_12
## t = -8.3476, df = 214, p-value = 8.637e-15
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.5900685 -0.3877780
## sample estimates:
##        cor 
## -0.4956151
cor.test(proj3$white_per_k_12, proj3$latinx_per_k_12, method="pearson",use="complete.obs")
## 
##  Pearson's product-moment correlation
## 
## data:  proj3$white_per_k_12 and proj3$latinx_per_k_12
## t = -27.856, df = 214, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.9111475 -0.8526147
## sample estimates:
##      cor 
## -0.88534

As expected, the assocation between white student enrollment and each variable attibuted to minorty student enrollment and/or tract population size is negative. Each of these tests are significant, but the largest and most pronounced assocation i seen among white and latinx school enrollment (-.89). Naturally, I run scatterplots and regression models to determine the unit of change for each association. Here, I only run models for those predictor variables that represent the proportion of residents in tract across each racial category. The only student enrollment vaiable I use going forward is my dependent variable, white student enrollment.

#Scatterplots and Regressions
model1 <- lm(white_per_k_12~black_per_pop, data=proj3)
model2 <- lm(white_per_k_12~latinx_per_pop, data=proj3)
model3 <- lm(white_per_k_12~white_per_pop, data=proj3)


equation = function(x) {
  lm_coef <- list(a = round(coef(x)[1], digits = 2),
                  b = round(coef(x)[2], digits = 2),
                  r2 = round(summary(x)$r.squared, digits = 2));
  lm_eq <- substitute(italic(y) == a + b %.% italic(x)*","~~italic(R)^2~"="~r2,lm_coef)
  as.character(as.expression(lm_eq));                 
}

m1 <- ggplot(proj3, aes(x=white_per_k_12, y=black_per_pop)) + geom_point(shape=1) + geom_smooth(method=lm, se=FALSE) +
      ggtitle("Associating Blacks in Tract and Whites Enrolled: Source: ACS 2013-2017") +
      scale_x_continuous(name = "White Children Enrolled in School K-12") +
      scale_y_continuous(name = "Black Residents in Tract") +
      annotate("rect", xmin = 0.00, xmax = 0.1, ymin = -0.056, ymax = -0.044, fill="white", colour="red") +
      annotate("text", x = 0.05, y = -0.05, label = equation(model1), parse = TRUE) 

m2 <- ggplot(proj3, aes(x=white_per_k_12, y=latinx_per_pop)) + geom_point(shape=1) + geom_smooth(method=lm, se=FALSE) +
      ggtitle("Associating Latinx in Tract and Whites Enrolled: Source: ACS 2013-2017") +
      scale_x_continuous(name = "White Children Enrolled in School K-12") +
      scale_y_continuous(name = "Latinx Residents in Tract") +
      annotate("rect", xmin = 0.00, xmax = 0.1, ymin = -0.056, ymax = -0.044, fill="white", colour="red") +
      annotate("text", x = 0.05, y = -0.05, label = equation(model2), parse = TRUE)

m3 <- ggplot(proj3, aes(x=white_per_k_12, y=white_per_pop)) + geom_point(shape=1) + geom_smooth(method=lm, se=FALSE) +
      ggtitle("Associating Whites in Tract and Whites Enrolled: Source: ACS 2013-2017") +
      scale_x_continuous(name = "White Children Enrolled in School K-12") +
      scale_y_continuous(name = "White Residents in Tract") +
      annotate("rect", xmin = 0.00, xmax = 0.1, ymin = -0.056, ymax = -0.044, fill="white", colour="red") +
      annotate("text", x = 0.05, y = -0.05, label = equation(model3), parse = TRUE)


m1
## Warning: Removed 2 rows containing non-finite values (stat_smooth).
## Warning: Removed 2 rows containing missing values (geom_point).

m2
## Warning: Removed 2 rows containing non-finite values (stat_smooth).

## Warning: Removed 2 rows containing missing values (geom_point).

m3
## Warning: Removed 2 rows containing non-finite values (stat_smooth).

## Warning: Removed 2 rows containing missing values (geom_point).

model1 <- lm(white_per_k_12~black_per_pop, data=proj3)
summary(model1)
## 
## Call:
## lm(formula = white_per_k_12 ~ black_per_pop, data = proj3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.44996 -0.19903 -0.01124  0.21098  0.53482 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.52980    0.02271  23.326   <2e-16 ***
## black_per_pop -1.96328    0.20304  -9.669   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2461 on 214 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.3041, Adjusted R-squared:  0.3008 
## F-statistic:  93.5 on 1 and 214 DF,  p-value: < 2.2e-16
model2 <- lm(white_per_k_12~latinx_per_pop, data=proj3)
summary(model2)
## 
## Call:
## lm(formula = white_per_k_12 ~ latinx_per_pop, data = proj3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.54576 -0.10982  0.02302  0.11546  0.49314 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.75512    0.02034   37.12   <2e-16 ***
## latinx_per_pop -1.14654    0.05223  -21.95   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1636 on 214 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.6924, Adjusted R-squared:  0.691 
## F-statistic: 481.8 on 1 and 214 DF,  p-value: < 2.2e-16
model3 <- lm(white_per_k_12~black_per_pop+latinx_per_pop, data=proj3)
summary(model3)
## 
## Call:
## lm(formula = white_per_k_12 ~ black_per_pop + latinx_per_pop, 
##     data = proj3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.53526 -0.09409  0.01337  0.09282  0.46018 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.79172    0.01786   44.34   <2e-16 ***
## black_per_pop  -1.09523    0.12238   -8.95   <2e-16 ***
## latinx_per_pop -1.00485    0.04736  -21.22   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1398 on 213 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.7765, Adjusted R-squared:  0.7744 
## F-statistic:   370 on 2 and 213 DF,  p-value: < 2.2e-16
model4 <- lm(white_per_k_12~black_per_pop+latinx_per_pop+white_per_pop, data=proj3)
summary(model4)
## 
## Call:
## lm(formula = white_per_k_12 ~ black_per_pop + latinx_per_pop + 
##     white_per_pop, data = proj3)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.42044 -0.08201  0.01131  0.07608  0.52917 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     0.04349    0.11986   0.363   0.7171    
## black_per_pop  -0.24409    0.17582  -1.388   0.1665    
## latinx_per_pop -0.26756    0.12484  -2.143   0.0332 *  
## white_per_pop   0.86407    0.13711   6.302 1.67e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1286 on 212 degrees of freedom
##   (2 observations deleted due to missingness)
## Multiple R-squared:  0.8118, Adjusted R-squared:  0.8091 
## F-statistic: 304.7 on 3 and 212 DF,  p-value: < 2.2e-16

This is interesting. I run four models. The first demonstrates the individual relationship between black populaiton in tract and white student enrollment (model 1) and the second, latinx population in tract and white student enrollment. Both models show that every unit increase in black inhabitants in the tract corresponds with a subsequent decrease in white student enrollment. The R^2 is much larger however for latinx, at almost 70 percent contrast to blacks, 30 percent. The third models includes both variables as they explain white student enrollment. The R^2 is relatively high at 77 percent, and the coefficent is once again higher when controlling for the proportion of black populations in tract (though the standard error is higher). Lastly, the final model includes black, white and latinx population in tract as they work to predict white student enrollment. Naturally, the positive assocation between the proportion of white students enrolled and the proporiton of whites living in tract is high. As it relates to black inhabitancy, the effect is no longer significant, and is only barely significant for latinx inhabtancy.

Conclusion

This report speaks to the constant prevalence of segregation in the state of Texas, and in particular, the current migratory patterns of residents in Travis County. It is possible that the influx of black migrants into suburban cities could be triggering this response, assuming that the proportion of black students attending schools is increasing in line with their respective population. Also, tracts carrying large population shares of black residents are likely residentially segregated, and if white residents living in the tract are of higher ses, research suggests that they are likely to send their children to schools outside the district. This may explain the negative association.

The Latinx populatin in Travis county continues to increase substantially. The fact that tracts carrying significant populations of latinx residents are strongly correlated with a subsequent decrease in white student enrollment is not much different than the black association. But one wonders how long this trend can persist given the aforementioned growing increase of latinx inhabitancy.

One huge limitation to this project is the large margin of errors seens across the variables. Being that this is the ACS, reliability is not as assured as the census.

#Changing the variable names. Total enrollment by grade
project1$total_kinder<-project1$AH0TE004
project1$total_1st<-project1$AH0TE005
project1$total_2nd<-project1$AH0TE006
project1$total_3rd<-project1$AH0TE007
project1$total_4th<-project1$AH0TE008
project1$total_5th<-project1$AH0TE009
project1$total_6th<-project1$AH0TE010
project1$total_7th<-project1$AH0TE011
project1$total_8th<-project1$AH0TE012
project1$total_9th<-project1$AH0TE013
project1$total_10th<-project1$AH0TE014
project1$total_11th<-project1$AH0TE015
project1$total_12th<-project1$AH0TE016

#Changing the variable names. Total enrollment by grade (margin of error)
project1$total_kindererror<-project1$AH0TM004
project1$total_1sterror<-project1$AH0TM005
project1$total_2nderror<-project1$AH0TM006
project1$total_3rderror<-project1$AH0TM007
project1$total_4therror<-project1$AH0TM008
project1$total_5therror<-project1$AH0TM009
project1$total_6therror<-project1$AH0TM010
project1$total_7therror<-project1$AH0TM011
project1$total_8therror<-project1$AH0TM012
project1$total_9therror<-project1$AH0TM013
project1$total_10therror<-project1$AH0TM014
project1$total_11therror<-project1$AH0TM015
project1$total_12therror<-project1$AH0TM016

attach(project1)
## The following objects are masked from proj3:
## 
##     AH01E001, AH01E002, AH01E003, AH01E004, AH01E005, AH01E006,
##     AH01E007, AH01E008, AH01E009, AH01E010, AH01E011, AH01E012,
##     AH01E013, AH01E014, AH01E015, AH01E016, AH01E017, AH01E018,
##     AH01E019, AH01M001, AH01M002, AH01M003, AH01M004, AH01M005,
##     AH01M006, AH01M007, AH01M008, AH01M009, AH01M010, AH01M011,
##     AH01M012, AH01M013, AH01M014, AH01M015, AH01M016, AH01M017,
##     AH01M018, AH01M019, AH02E001, AH02E002, AH02E003, AH02E004,
##     AH02E005, AH02E006, AH02E007, AH02E008, AH02E009, AH02E010,
##     AH02E011, AH02E012, AH02E013, AH02E014, AH02E015, AH02E016,
##     AH02E017, AH02E018, AH02E019, AH02M001, AH02M002, AH02M003,
##     AH02M004, AH02M005, AH02M006, AH02M007, AH02M008, AH02M009,
##     AH02M010, AH02M011, AH02M012, AH02M013, AH02M014, AH02M015,
##     AH02M016, AH02M017, AH02M018, AH02M019, AH0TE001, AH0TE002,
##     AH0TE003, AH0TE004, AH0TE005, AH0TE006, AH0TE007, AH0TE008,
##     AH0TE009, AH0TE010, AH0TE011, AH0TE012, AH0TE013, AH0TE014,
##     AH0TE015, AH0TE016, AH0TE017, AH0TE018, AH0TE019, AH0TM001,
##     AH0TM002, AH0TM003, AH0TM004, AH0TM005, AH0TM006, AH0TM007,
##     AH0TM008, AH0TM009, AH0TM010, AH0TM011, AH0TM012, AH0TM013,
##     AH0TM014, AH0TM015, AH0TM016, AH0TM017, AH0TM018, AH0TM019,
##     AH0VE001, AH0VE002, AH0VE003, AH0VE004, AH0VE005, AH0VE006,
##     AH0VE007, AH0VE008, AH0VE009, AH0VE010, AH0VE011, AH0VE012,
##     AH0VE013, AH0VE014, AH0VE015, AH0VE016, AH0VE017, AH0VE018,
##     AH0VE019, AH0VM001, AH0VM002, AH0VM003, AH0VM004, AH0VM005,
##     AH0VM006, AH0VM007, AH0VM008, AH0VM009, AH0VM010, AH0VM011,
##     AH0VM012, AH0VM013, AH0VM014, AH0VM015, AH0VM016, AH0VM017,
##     AH0VM018, AH0VM019, AH1PE001, AH1PM001, AHYQE001, AHYQE002,
##     AHYQE003, AHYQE004, AHYQE005, AHYQE006, AHYQE007, AHYQE008,
##     AHYQE009, AHYQE010, AHYQE011, AHYQE012, AHYQE013, AHYQE014,
##     AHYQE015, AHYQE016, AHYQE017, AHYQE018, AHYQE019, AHYQE020,
##     AHYQE021, AHYQE022, AHYQE023, AHYQE024, AHYQE025, AHYQE026,
##     AHYQE027, AHYQE028, AHYQE029, AHYQE030, AHYQE031, AHYQE032,
##     AHYQE033, AHYQE034, AHYQE035, AHYQE036, AHYQE037, AHYQE038,
##     AHYQE039, AHYQE040, AHYQE041, AHYQE042, AHYQE043, AHYQE044,
##     AHYQE045, AHYQE046, AHYQE047, AHYQE048, AHYQE049, AHYQM001,
##     AHYQM002, AHYQM003, AHYQM004, AHYQM005, AHYQM006, AHYQM007,
##     AHYQM008, AHYQM009, AHYQM010, AHYQM011, AHYQM012, AHYQM013,
##     AHYQM014, AHYQM015, AHYQM016, AHYQM017, AHYQM018, AHYQM019,
##     AHYQM020, AHYQM021, AHYQM022, AHYQM023, AHYQM024, AHYQM025,
##     AHYQM026, AHYQM027, AHYQM028, AHYQM029, AHYQM030, AHYQM031,
##     AHYQM032, AHYQM033, AHYQM034, AHYQM035, AHYQM036, AHYQM037,
##     AHYQM038, AHYQM039, AHYQM040, AHYQM041, AHYQM042, AHYQM043,
##     AHYQM044, AHYQM045, AHYQM046, AHYQM047, AHYQM048, AHYQM049,
##     AHZAE001, AHZAE002, AHZAE003, AHZAE004, AHZAE005, AHZAE006,
##     AHZAE007, AHZAE008, AHZAE009, AHZAE010, AHZAE011, AHZAE012,
##     AHZAE013, AHZAE014, AHZAE015, AHZAE016, AHZAE017, AHZAE018,
##     AHZAE019, AHZAE020, AHZAE021, AHZAM001, AHZAM002, AHZAM003,
##     AHZAM004, AHZAM005, AHZAM006, AHZAM007, AHZAM008, AHZAM009,
##     AHZAM010, AHZAM011, AHZAM012, AHZAM013, AHZAM014, AHZAM015,
##     AHZAM016, AHZAM017, AHZAM018, AHZAM019, AHZAM020, AHZAM021,
##     AIANHHA.x, AIANHHA.y, AITSCEA.x, AITSCEA.y, ANRCA.x, ANRCA.y,
##     bk_12, black_per_k_12, black_per_pop, black_pop, BLKGRPA.x,
##     BLKGRPA.y, BTBGA.x, BTBGA.y, BTTRA.x, BTTRA.y, CBSAA.x,
##     CBSAA.y, CDCURRA.x, CDCURRA.y, CNECTAA.x, CNECTAA.y,
##     CONCITA.x, CONCITA.y, COUNTY.x, COUNTY.y, COUNTYA.x,
##     COUNTYA.y, COUSUBA.x, COUSUBA.y, CSAA.x, CSAA.y, DIVISIONA.x,
##     DIVISIONA.y, GISJOIN, k_12, latinx_per_k_12, latinx_per_pop,
##     latinx_pop, lk_12, METDIVA.x, METDIVA.y, NAME_E.x, NAME_E.y,
##     NAME_M.x, NAME_M.y, NECTAA.x, NECTAA.y, NECTADIVA.x,
##     NECTADIVA.y, PLACEA.x, PLACEA.y, PUMA5A.x, PUMA5A.y,
##     REGIONA.x, REGIONA.y, RES_ONLYA.x, RES_ONLYA.y, SDELMA.x,
##     SDELMA.y, SDSECA.x, SDSECA.y, SDUNIA.x, SDUNIA.y, SLDLA.x,
##     SLDLA.y, SLDUA.x, SLDUA.y, STATE.x, STATE.y, STATEA.x,
##     STATEA.y, SUBMCDA.x, SUBMCDA.y, total_pop, TRACTA.x, TRACTA.y,
##     TRUSTA.x, TRUSTA.y, UAA.x, UAA.y, white_per_k_12,
##     white_per_pop, white_pop, wk_12, YEAR.x, YEAR.y, ZCTA5A.x,
##     ZCTA5A.y
total<-cbind(total_kinder,total_kindererror,total_1st,total_1sterror,total_2nd,total_2nderror,total_3rd,total_3rderror,total_4th,total_4therror,total_5th,total_5therror,total_6th,total_6therror,total_7th,total_7therror,total_8th,total_8therror,total_9th,total_9therror,total_10th,total_10therror,total_11th,total_11therror,total_12th,total_12therror)
## The following objects are masked from project1 (pos = 3):
## 
##     AH01E001, AH01E002, AH01E003, AH01E004, AH01E005, AH01E006,
##     AH01E007, AH01E008, AH01E009, AH01E010, AH01E011, AH01E012,
##     AH01E013, AH01E014, AH01E015, AH01E016, AH01E017, AH01E018,
##     AH01E019, AH01M001, AH01M002, AH01M003, AH01M004, AH01M005,
##     AH01M006, AH01M007, AH01M008, AH01M009, AH01M010, AH01M011,
##     AH01M012, AH01M013, AH01M014, AH01M015, AH01M016, AH01M017,
##     AH01M018, AH01M019, AH02E001, AH02E002, AH02E003, AH02E004,
##     AH02E005, AH02E006, AH02E007, AH02E008, AH02E009, AH02E010,
##     AH02E011, AH02E012, AH02E013, AH02E014, AH02E015, AH02E016,
##     AH02E017, AH02E018, AH02E019, AH02M001, AH02M002, AH02M003,
##     AH02M004, AH02M005, AH02M006, AH02M007, AH02M008, AH02M009,
##     AH02M010, AH02M011, AH02M012, AH02M013, AH02M014, AH02M015,
##     AH02M016, AH02M017, AH02M018, AH02M019, AH0TE001, AH0TE002,
##     AH0TE003, AH0TE004, AH0TE005, AH0TE006, AH0TE007, AH0TE008,
##     AH0TE009, AH0TE010, AH0TE011, AH0TE012, AH0TE013, AH0TE014,
##     AH0TE015, AH0TE016, AH0TE017, AH0TE018, AH0TE019, AH0TM001,
##     AH0TM002, AH0TM003, AH0TM004, AH0TM005, AH0TM006, AH0TM007,
##     AH0TM008, AH0TM009, AH0TM010, AH0TM011, AH0TM012, AH0TM013,
##     AH0TM014, AH0TM015, AH0TM016, AH0TM017, AH0TM018, AH0TM019,
##     AH0VE001, AH0VE002, AH0VE003, AH0VE004, AH0VE005, AH0VE006,
##     AH0VE007, AH0VE008, AH0VE009, AH0VE010, AH0VE011, AH0VE012,
##     AH0VE013, AH0VE014, AH0VE015, AH0VE016, AH0VE017, AH0VE018,
##     AH0VE019, AH0VM001, AH0VM002, AH0VM003, AH0VM004, AH0VM005,
##     AH0VM006, AH0VM007, AH0VM008, AH0VM009, AH0VM010, AH0VM011,
##     AH0VM012, AH0VM013, AH0VM014, AH0VM015, AH0VM016, AH0VM017,
##     AH0VM018, AH0VM019, AH1PE001, AH1PM001, AHYQE001, AHYQE002,
##     AHYQE003, AHYQE004, AHYQE005, AHYQE006, AHYQE007, AHYQE008,
##     AHYQE009, AHYQE010, AHYQE011, AHYQE012, AHYQE013, AHYQE014,
##     AHYQE015, AHYQE016, AHYQE017, AHYQE018, AHYQE019, AHYQE020,
##     AHYQE021, AHYQE022, AHYQE023, AHYQE024, AHYQE025, AHYQE026,
##     AHYQE027, AHYQE028, AHYQE029, AHYQE030, AHYQE031, AHYQE032,
##     AHYQE033, AHYQE034, AHYQE035, AHYQE036, AHYQE037, AHYQE038,
##     AHYQE039, AHYQE040, AHYQE041, AHYQE042, AHYQE043, AHYQE044,
##     AHYQE045, AHYQE046, AHYQE047, AHYQE048, AHYQE049, AHYQM001,
##     AHYQM002, AHYQM003, AHYQM004, AHYQM005, AHYQM006, AHYQM007,
##     AHYQM008, AHYQM009, AHYQM010, AHYQM011, AHYQM012, AHYQM013,
##     AHYQM014, AHYQM015, AHYQM016, AHYQM017, AHYQM018, AHYQM019,
##     AHYQM020, AHYQM021, AHYQM022, AHYQM023, AHYQM024, AHYQM025,
##     AHYQM026, AHYQM027, AHYQM028, AHYQM029, AHYQM030, AHYQM031,
##     AHYQM032, AHYQM033, AHYQM034, AHYQM035, AHYQM036, AHYQM037,
##     AHYQM038, AHYQM039, AHYQM040, AHYQM041, AHYQM042, AHYQM043,
##     AHYQM044, AHYQM045, AHYQM046, AHYQM047, AHYQM048, AHYQM049,
##     AHZAE001, AHZAE002, AHZAE003, AHZAE004, AHZAE005, AHZAE006,
##     AHZAE007, AHZAE008, AHZAE009, AHZAE010, AHZAE011, AHZAE012,
##     AHZAE013, AHZAE014, AHZAE015, AHZAE016, AHZAE017, AHZAE018,
##     AHZAE019, AHZAE020, AHZAE021, AHZAM001, AHZAM002, AHZAM003,
##     AHZAM004, AHZAM005, AHZAM006, AHZAM007, AHZAM008, AHZAM009,
##     AHZAM010, AHZAM011, AHZAM012, AHZAM013, AHZAM014, AHZAM015,
##     AHZAM016, AHZAM017, AHZAM018, AHZAM019, AHZAM020, AHZAM021,
##     AIANHHA.x, AIANHHA.y, AITSCEA.x, AITSCEA.y, ANRCA.x, ANRCA.y,
##     bk_12, black_per_k_12, black_per_pop, black_pop, BLKGRPA.x,
##     BLKGRPA.y, BTBGA.x, BTBGA.y, BTTRA.x, BTTRA.y, CBSAA.x,
##     CBSAA.y, CDCURRA.x, CDCURRA.y, CNECTAA.x, CNECTAA.y,
##     CONCITA.x, CONCITA.y, COUNTY.x, COUNTY.y, COUNTYA.x,
##     COUNTYA.y, COUSUBA.x, COUSUBA.y, CSAA.x, CSAA.y, DIVISIONA.x,
##     DIVISIONA.y, GISJOIN, k_12, latinx_per_k_12, latinx_per_pop,
##     latinx_pop, lk_12, METDIVA.x, METDIVA.y, NAME_E.x, NAME_E.y,
##     NAME_M.x, NAME_M.y, NECTAA.x, NECTAA.y, NECTADIVA.x,
##     NECTADIVA.y, PLACEA.x, PLACEA.y, PUMA5A.x, PUMA5A.y,
##     REGIONA.x, REGIONA.y, RES_ONLYA.x, RES_ONLYA.y, SDELMA.x,
##     SDELMA.y, SDSECA.x, SDSECA.y, SDUNIA.x, SDUNIA.y, SLDLA.x,
##     SLDLA.y, SLDUA.x, SLDUA.y, STATE.x, STATE.y, STATEA.x,
##     STATEA.y, SUBMCDA.x, SUBMCDA.y, total_10th, total_10therror,
##     total_11th, total_11therror, total_12th, total_12therror,
##     total_1st, total_1sterror, total_2nd, total_2nderror,
##     total_3rd, total_3rderror, total_4th, total_4therror,
##     total_5th, total_5therror, total_6th, total_6therror,
##     total_7th, total_7therror, total_8th, total_8therror,
##     total_9th, total_9therror, total_kinder, total_kindererror,
##     total_pop, TRACTA.x, TRACTA.y, TRUSTA.x, TRUSTA.y, UAA.x,
##     UAA.y, white_per_k_12, white_per_pop, white_pop, wk_12,
##     YEAR.x, YEAR.y, ZCTA5A.x, ZCTA5A.y
## The following objects are masked from proj3:
## 
##     AH01E001, AH01E002, AH01E003, AH01E004, AH01E005, AH01E006,
##     AH01E007, AH01E008, AH01E009, AH01E010, AH01E011, AH01E012,
##     AH01E013, AH01E014, AH01E015, AH01E016, AH01E017, AH01E018,
##     AH01E019, AH01M001, AH01M002, AH01M003, AH01M004, AH01M005,
##     AH01M006, AH01M007, AH01M008, AH01M009, AH01M010, AH01M011,
##     AH01M012, AH01M013, AH01M014, AH01M015, AH01M016, AH01M017,
##     AH01M018, AH01M019, AH02E001, AH02E002, AH02E003, AH02E004,
##     AH02E005, AH02E006, AH02E007, AH02E008, AH02E009, AH02E010,
##     AH02E011, AH02E012, AH02E013, AH02E014, AH02E015, AH02E016,
##     AH02E017, AH02E018, AH02E019, AH02M001, AH02M002, AH02M003,
##     AH02M004, AH02M005, AH02M006, AH02M007, AH02M008, AH02M009,
##     AH02M010, AH02M011, AH02M012, AH02M013, AH02M014, AH02M015,
##     AH02M016, AH02M017, AH02M018, AH02M019, AH0TE001, AH0TE002,
##     AH0TE003, AH0TE004, AH0TE005, AH0TE006, AH0TE007, AH0TE008,
##     AH0TE009, AH0TE010, AH0TE011, AH0TE012, AH0TE013, AH0TE014,
##     AH0TE015, AH0TE016, AH0TE017, AH0TE018, AH0TE019, AH0TM001,
##     AH0TM002, AH0TM003, AH0TM004, AH0TM005, AH0TM006, AH0TM007,
##     AH0TM008, AH0TM009, AH0TM010, AH0TM011, AH0TM012, AH0TM013,
##     AH0TM014, AH0TM015, AH0TM016, AH0TM017, AH0TM018, AH0TM019,
##     AH0VE001, AH0VE002, AH0VE003, AH0VE004, AH0VE005, AH0VE006,
##     AH0VE007, AH0VE008, AH0VE009, AH0VE010, AH0VE011, AH0VE012,
##     AH0VE013, AH0VE014, AH0VE015, AH0VE016, AH0VE017, AH0VE018,
##     AH0VE019, AH0VM001, AH0VM002, AH0VM003, AH0VM004, AH0VM005,
##     AH0VM006, AH0VM007, AH0VM008, AH0VM009, AH0VM010, AH0VM011,
##     AH0VM012, AH0VM013, AH0VM014, AH0VM015, AH0VM016, AH0VM017,
##     AH0VM018, AH0VM019, AH1PE001, AH1PM001, AHYQE001, AHYQE002,
##     AHYQE003, AHYQE004, AHYQE005, AHYQE006, AHYQE007, AHYQE008,
##     AHYQE009, AHYQE010, AHYQE011, AHYQE012, AHYQE013, AHYQE014,
##     AHYQE015, AHYQE016, AHYQE017, AHYQE018, AHYQE019, AHYQE020,
##     AHYQE021, AHYQE022, AHYQE023, AHYQE024, AHYQE025, AHYQE026,
##     AHYQE027, AHYQE028, AHYQE029, AHYQE030, AHYQE031, AHYQE032,
##     AHYQE033, AHYQE034, AHYQE035, AHYQE036, AHYQE037, AHYQE038,
##     AHYQE039, AHYQE040, AHYQE041, AHYQE042, AHYQE043, AHYQE044,
##     AHYQE045, AHYQE046, AHYQE047, AHYQE048, AHYQE049, AHYQM001,
##     AHYQM002, AHYQM003, AHYQM004, AHYQM005, AHYQM006, AHYQM007,
##     AHYQM008, AHYQM009, AHYQM010, AHYQM011, AHYQM012, AHYQM013,
##     AHYQM014, AHYQM015, AHYQM016, AHYQM017, AHYQM018, AHYQM019,
##     AHYQM020, AHYQM021, AHYQM022, AHYQM023, AHYQM024, AHYQM025,
##     AHYQM026, AHYQM027, AHYQM028, AHYQM029, AHYQM030, AHYQM031,
##     AHYQM032, AHYQM033, AHYQM034, AHYQM035, AHYQM036, AHYQM037,
##     AHYQM038, AHYQM039, AHYQM040, AHYQM041, AHYQM042, AHYQM043,
##     AHYQM044, AHYQM045, AHYQM046, AHYQM047, AHYQM048, AHYQM049,
##     AHZAE001, AHZAE002, AHZAE003, AHZAE004, AHZAE005, AHZAE006,
##     AHZAE007, AHZAE008, AHZAE009, AHZAE010, AHZAE011, AHZAE012,
##     AHZAE013, AHZAE014, AHZAE015, AHZAE016, AHZAE017, AHZAE018,
##     AHZAE019, AHZAE020, AHZAE021, AHZAM001, AHZAM002, AHZAM003,
##     AHZAM004, AHZAM005, AHZAM006, AHZAM007, AHZAM008, AHZAM009,
##     AHZAM010, AHZAM011, AHZAM012, AHZAM013, AHZAM014, AHZAM015,
##     AHZAM016, AHZAM017, AHZAM018, AHZAM019, AHZAM020, AHZAM021,
##     AIANHHA.x, AIANHHA.y, AITSCEA.x, AITSCEA.y, ANRCA.x, ANRCA.y,
##     bk_12, black_per_k_12, black_per_pop, black_pop, BLKGRPA.x,
##     BLKGRPA.y, BTBGA.x, BTBGA.y, BTTRA.x, BTTRA.y, CBSAA.x,
##     CBSAA.y, CDCURRA.x, CDCURRA.y, CNECTAA.x, CNECTAA.y,
##     CONCITA.x, CONCITA.y, COUNTY.x, COUNTY.y, COUNTYA.x,
##     COUNTYA.y, COUSUBA.x, COUSUBA.y, CSAA.x, CSAA.y, DIVISIONA.x,
##     DIVISIONA.y, GISJOIN, k_12, latinx_per_k_12, latinx_per_pop,
##     latinx_pop, lk_12, METDIVA.x, METDIVA.y, NAME_E.x, NAME_E.y,
##     NAME_M.x, NAME_M.y, NECTAA.x, NECTAA.y, NECTADIVA.x,
##     NECTADIVA.y, PLACEA.x, PLACEA.y, PUMA5A.x, PUMA5A.y,
##     REGIONA.x, REGIONA.y, RES_ONLYA.x, RES_ONLYA.y, SDELMA.x,
##     SDELMA.y, SDSECA.x, SDSECA.y, SDUNIA.x, SDUNIA.y, SLDLA.x,
##     SLDLA.y, SLDUA.x, SLDUA.y, STATE.x, STATE.y, STATEA.x,
##     STATEA.y, SUBMCDA.x, SUBMCDA.y, total_pop, TRACTA.x, TRACTA.y,
##     TRUSTA.x, TRUSTA.y, UAA.x, UAA.y, white_per_k_12,
##     white_per_pop, white_pop, wk_12, YEAR.x, YEAR.y, ZCTA5A.x,
##     ZCTA5A.y
test.
total_kinder total_kindererror total_1st total_1sterror total_2nd total_2nderror total_3rd total_3rderror total_4th total_4therror total_5th total_5therror total_6th total_6therror total_7th total_7therror total_8th total_8therror total_9th total_9therror total_10th total_10therror total_11th total_11therror total_12th total_12therror
17 22 26 29 7 11 34 30 18 21 11 13 51 37 9 11 8 9 24 23 95 45 14 15 16 22
53 33 57 41 29 24 18 20 41 37 50 43 46 33 34 31 19 18 18 27 52 52 16 16 30 26
68 49 35 48 56 53 111 83 181 88 7 15 32 31 15 18 27 28 30 36 67 35 35 37 14 16
57 54 11 17 43 34 87 58 18 22 51 46 130 106 90 69 68 74 59 34 44 46 31 25 41 34
190 155 44 67 238 159 131 106 162 115 65 70 182 141 241 159 170 132 128 103 139 105 176 94 60 73
22 26 81 66 77 61 21 30 38 48 75 52 17 19 86 57 54 44 84 70 59 40 63 49 98 65
24 28 25 49 24 35 54 69 79 59 52 67 63 59 82 69 34 41 57 55 92 57 6 11 17 28
43 33 30 29 40 30 35 35 70 46 32 36 58 35 38 46 71 42 63 41 64 45 29 28 36 26
304 125 176 94 157 93 143 105 66 55 339 133 106 82 127 106 156 103 245 125 318 158 121 81 279 187
61 54 105 70 70 65 70 86 0 16 38 39 81 86 96 75 29 36 69 74 157 94 95 85 63 68
90 51 17 21 1 3 97 75 10 17 5 9 55 40 46 49 38 38 1 5 34 38 34 29 33 38
19 21 41 31 57 36 14 16 62 58 15 18 57 55 45 32 10 14 42 46 34 35 19 24 35 35
11 18 30 40 92 72 17 27 10 16 47 41 26 44 59 58 94 57 30 39 0 11 43 51 35 55
80 68 0 11 28 33 79 67 22 31 40 42 20 34 21 27 80 77 71 57 11 19 20 24 22 34
233 112 57 70 155 104 118 91 126 137 135 98 155 156 113 71 157 121 150 104 203 154 73 78 84 87
39 37 35 33 60 46 87 62 95 77 64 44 34 41 45 61 34 31 63 60 143 101 82 69 9 14
64 54 70 56 91 69 66 47 102 71 63 50 104 68 22 30 69 73 49 56 29 32 13 22 77 84
102 96 91 80 82 88 14 38 86 53 64 65 48 51 97 81 0 11 47 64 54 47 31 52 118 115
115 68 72 52 113 69 143 83 110 85 89 59 84 49 167 84 104 56 79 58 103 59 158 101 214 116
234 129 295 212 461 230 244 201 283 205 137 98 330 153 171 111 362 197 255 164 315 162 183 123 405 230
38 36 108 89 117 84 82 71 63 52 190 124 181 104 190 103 84 56 81 65 57 55 99 83 75 61
38 44 108 96 125 93 114 94 214 137 22 36 98 73 170 131 125 107 126 86 106 95 153 111 241 160
21 35 67 79 88 69 30 49 106 101 39 54 174 143 62 57 129 119 74 64 233 130 85 90 200 128
35 31 61 45 36 39 17 19 68 42 65 47 36 29 112 64 39 37 92 49 157 68 13 19 107 62
44 45 90 81 45 49 28 34 91 67 53 52 96 63 135 91 102 98 117 78 85 63 69 56 87 62
257 121 80 83 96 88 54 45 140 95 44 39 54 45 96 101 70 54 56 39 114 63 35 36 154 149

project1\(black_kinder<-project1\)AH0TE004 project1\(black_1st<-project1\)AH0TE005 project1\(black_2nd<-project1\)AH0TE006 project1\(black_3rd<-project1\)AH0TE007 project1\(black_4th<-project1\)AH0TE008 project1\(black_5th<-project1\)AH0TE009 project1\(black_6th<-project1\)AH0TE010 project1\(black_7th<-project1\)AH0TE011 project1\(black_8th<-project1\)AH0TE012 project1\(black_9th<-project1\)AH0TE013 project1\(black_10th<-project1\)AH0TE014 project1\(black_11th<-project1\)AH0TE015 project1\(black_12th<-project1\)AH0TE016

project1\(k_12<-project1\)AH0TE004+project1\(AH0TE005+project1\)AH0TE006+project1\(AH0TE007+project1\)AH0TE008+project1\(AH0TE009+project1\)AH0TE010+project1\(AH0TE011+project1\)AH0TE012+project1\(AH0TE013+project1\)AH0TE014+project1\(AH0TE015+project1\)AH0TE016

#total amount of black students enrolled in primary school in the tract project1\(bk_12<-project1\)AH0VE004+project1\(AH0VE005+project1\)AH0VE006+project1\(AH0VE007+project1\)AH0VE008+project1\(AH0VE009+project1\)AH0VE010+project1\(AH0VE011+project1\)AH0VE012+project1\(AH0VE013+project1\)AH0VE014+project1\(AH0VE015+project1\)AH0VE016

#total amount of white students enrolled in primary school in the tract project1\(wk_12<-project1\)AH01E004+project1\(AH01E005+project1\)AH01E006+project1\(AH01E007+project1\)AH01E008+project1\(AH01E009+project1\)AH01E010+project1\(AH01E011+project1\)AH01E012+project1\(AH01E013+project1\)AH01E014+project1\(AH01E015+project1\)AH01E016

#total amount of latinx students enrolled in primary school in the tract project1\(lk_12<-project1\)AH02E004+project1\(AH02E005+project1\)AH02E006+project1\(AH02E007+project1\)AH02E008+project1\(AH02E009+project1\)AH02E010+project1\(AH02E011+project1\)AH02E012+project1\(AH02E013+project1\)AH02E014+project1\(AH02E015+project1\)AH02E016 ```