10 Correlation Free Online FlashCards

What does a scatterplot display?

A scatterplot displays paired observations $x_i,y_i$ as points; the explanatory variable is usually horizontal and the response variable vertical.

Which four features should you examine in a scatterplot?

Describe its direction, form, strength, and unusual features such as outliers, clusters, gaps, or changes in spread.

What does covariance measure?

Covariance measures whether two variables tend to vary together, but its numerical value depends on their measurement units.

What is the sample covariance formula?

The sample covariance is $s_{xy}=\frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})}{n-1}$.

How does Pearson correlation standardize covariance?

Pearson’s $r$ standardizes covariance by dividing it by the product of the variables’ standard deviations.

What is the possible range of Pearson’s $r$?

The value of $r$ must lie between $-1$ and $1$, inclusive.

What does the sign of $r$ indicate?

The sign indicates direction: positive means a positive linear association, and negative means a negative linear association.

What does $|r|$ indicate?

The absolute value $|r|$ indicates strength: values closer to 1 show stronger linear association, while values closer to 0 show weaker association.

Does $r=0$ rule out every relationship?

No. $r=0$ indicates no linear association, but a strong nonlinear relationship may still exist.

What hypotheses test for a nonzero population correlation?

Test $H_0:\rho=0$ against an alternative such as $H_a:\rho\ne0$, $H_a:\rho>0$, or $H_a:\rho<0$.

What test statistic is commonly used for correlation?

Use $t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$, compared with a $t$-distribution having $n-2$ degrees of freedom.

What does failing to reject $H_0$ mean?

Failing to reject $H_0$ means the sample lacks sufficient evidence of a nonzero population linear association; it does not prove $\rho=0$.