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Data-Centric Statistical Inference Using R and Tidyverse

Correlation Coefficient and Simpson's Paradox

Explore how the correlation coefficient remains unchanged under linear transformations and understand Simpson's Paradox. Learn to interpret contrasting results between aggregate and grouped data in multiple regression, focusing on the impact of confounding variables like credit limit on the relationship between credit card debt and income.

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Correlation coefficient

Recall that the correlation coefficient between income in thousands of dollars and credit card debt was 0.464. What if, instead, we looked at the correlation coefficient between income and credit card debt, but where income was in dollars and not thousands of dollars? This can be done by multiplying income by 1000.

R
credit_ch6 %>% select(debt, income) %>% 

mutate(income = income * 1000) %>% 

cor()

We say that the correlation coefficient is invariant to linear transformations. The correlation between xx and yy will be the same as the correlation between a⋅x+b ...