7.1 Correlation
To calculate the correlation coefficient (r
) between two numeric variables, use the cor.test()
function and specify the model as ~ Var1 + Var2
. This structure is unusual in that both variables follow the ~
, and the +
separates the two.
cor.test(~ ProfMath + ProfLang, dcps)
##
## Pearson's product-moment correlation
##
## data: ProfMath and ProfLang
## t = 22, df = 106, p-value <2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8691 0.9369
## sample estimates:
## cor
## 0.9088
Perhaps not surprisingly, the results suggest that math and language proficiency are positively and strongly correlated (\(r=0.91\)). It is unlikely we observe this association by chance alone (\(t=22.4\), \(p<0.001\)).
Use a scatterplot (plot()
) to visualize this bivariate association. Be sure to specify the formula as OutcomeVar ~ ExposureVar
:
plot(ProfMath ~ ProfLang, dcps)