## 34.6 Summary

In this chapter, correlation was used to describe the strength and direction of linear relationships between two quantitative variables.

Correlation coefficients (denoted $$r$$ in the sample; $$\rho$$ in the population) are always between $$-1$$ and $$+1$$.

Positive values denote positive relationships between the two variables: as one values gets larger, the other tends to get larger too.

Negative values denote negative relationships between the two variables: as one values gets larger, the other tends to get smaller. Values close to $$-1$$ or $$+1$$ are very strong relationships; values near zero shows very little linear relationship between the variables. Hypothesis tests for $$r$$ can be conducted using software.

Sometimes, $$R^2$$ is used to describe the relationship: it indicates what percentage of the variation in the response variable can be explained by knowing the value of the explanatory variables.

The following short video may help explain some of these concepts: