7 Correlation and Regression Free Online FlashCards

What does Pearson’s correlation coefficient measure?

Pearson’s correlation coefficient, written $r$, summarizes the direction and strength of a linear relationship between two quantitative variables.

What pattern does a positive correlation describe?

A positive correlation means larger values of one variable tend to occur with larger values of the other.

What does a correlation near zero indicate—and what might it miss?

A correlation near zero indicates little linear association, but a curved relationship may still exist.

What are two important properties of correlation?

Correlation has no units, and unusual observations can strongly affect its value.

Does correlation alone establish causation?

No. Correlation describes association, not cause and effect; a third factor may influence both variables.

What equation represents a simple linear regression model?

Simple linear regression models the average response with a straight line: $\widehat{y}=b_0+b_1x$.

How should you interpret a regression slope?

The slope $b_1$ estimates the change in predicted response for a one-unit increase in $x$, within the data’s context and range.

When is a regression intercept practically meaningful?

The intercept $b_0$ is the predicted response when $x=0$; it is meaningful only if zero is plausible and represented by the data.

What does the least-squares method minimize?

Least squares chooses the line that minimizes the sum of squared residuals; each residual is observed minus predicted.

What does $R^2$ describe?

$R^2$ is the proportion of response variation accounted for by the fitted model in the data used to fit it.

Does $R^2=0.72$ mean predictions are 72% accurate?

No. $R^2=0.72$ means the model accounts for 72% of observed response variation around its sample mean, not that predictions are 72% accurate.

What residual-plot pattern supports a straight-line model?

A suitable straight-line model generally has residuals scattered around zero without a systematic curve or changing spread.