SAT: Scatterplots & Modeling Glossary

The proportion (0 to 1) of the variance in $y$ explained by the model. Equals $r^2$ for simple linear regression.

A variable not included in the model that affects both $x$ and $y$, potentially creating a misleading association between them.

A measure from $-1$ to $1$ of the strength and direction of a linear association between two variables. $r > 0$ = positive, $r < 0$ = negative, $|r|$ near 1 = strong.

A model of the form $y = a \cdot b^t$ where $b > 1$ gives growth and $0 < b < 1$ gives decay. Characterized by constant percent change per unit time.

Using a model to predict $y$ for an $x$-value outside the range of the observed data. Less reliable than interpolation.

Using a model to predict $y$ for an $x$-value within the range of the observed data. Generally more reliable than extrapolation.

The least-squares regression line $\hat{y} = a + bx$ that minimizes the sum of the squared residuals for a set of data points.

The difference $e = y - \hat{y}$ between an observed value and the value predicted by a model.

A graph of residuals vs. $x$ (or vs. predicted values). Used to assess whether a linear model is appropriate.

A graph that displays ordered pairs $(x, y)$ as dots, showing the relationship between two quantitative variables.