Homework 5

d_vars <- district[, c("DAGC4X21R", "DPFVTOTK", "DPETECOP", "DPSTTOSA")]
# graduation rate, property wealth, % economically disadvantaged, and average teacher salary.

colnames(d_vars) <- c("Grad Rate", "Property Wealth", "% Low Income", "Teacher Salary")

cor(d_vars, use = "complete.obs")

##                   Grad Rate Property Wealth % Low Income Teacher Salary
## Grad Rate        1.00000000      0.04509333  -0.23574039    -0.01784474
## Property Wealth  0.04509333      1.00000000  -0.15595775     0.09702166
## % Low Income    -0.23574039     -0.15595775   1.00000000    -0.07348822
## Teacher Salary  -0.01784474      0.09702166  -0.07348822     1.00000000

pairs(d_vars)

cor.test(district$DPETECOP, district$DAGC4X21R, method = "pearson")

## 
##  Pearson's product-moment correlation
## 
## data:  district$DPETECOP and district$DAGC4X21R
## t = -7.968, df = 1072, p-value = 4.098e-15
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2921474 -0.1791774
## sample estimates:
##        cor 
## -0.2364613

cor.test(district$DPETECOP, district$DAGC4X21R, method = "spearman")

## Warning in cor.test.default(district$DPETECOP, district$DAGC4X21R, method =
## "spearman"): cannot compute exact p-value with ties

## 
##  Spearman's rank correlation rho
## 
## data:  district$DPETECOP and district$DAGC4X21R
## S = 271146333, p-value < 2.2e-16
## alternative hypothesis: true rho is not equal to 0
## sample estimates:
##        rho 
## -0.3132352

cor.test(district$DPETECOP, district$DAGC4X21R, method = "kendall")

## 
##  Kendall's rank correlation tau
## 
## data:  district$DPETECOP and district$DAGC4X21R
## z = -10.367, p-value < 2.2e-16
## alternative hypothesis: true tau is not equal to 0
## sample estimates:
##        tau 
## -0.2183232

# Most districts had graduation rates close to 100%, and many had exactly the same rate or tied rates, so I used Kendall’s tau. I found a statistically significant negative relationship between the share of low-income students and the four-year graduation rate (τ = -0.21, p < 0.001). Meaning districts with a higher share of low-income students tended to have lower graduation rates.