Linear Regression

The least-squares regression line of $y$ on $x$ has the form $y = a + bx$, where $b$ is the gradient and $a$ the intercept. It is the line that best fits the data by minimising the vertical distances to the points.

In context, $b$ is the predicted $\textbf{change in the response}$ for each one-unit increase in the explanatory variable, and $a$ is the predicted response when $x = 0$. Always state units.

Predicting $\textbf{within}$ the data range ($\textbf{interpolation}$) is reliable. Predicting $\textbf{outside}$ it ($\textbf{extrapolation}$) is unreliable, because the linear pattern may not continue.