Linear model

A linear model summarizes a scatterplot with one straight line, so any $x$ you choose turns into a prediction. It is written $\hat{y} = a + bx$, where $\hat{y}$ (read y-hat) is the predicted response, $a$ is the y-intercept, and $b$ is the slope. For example, if $\hat{y} = 12 + 3x$ predicts a plant's height in centimeters from weeks of growth, then at $x = 5$ weeks the model gives $12 + 3(5) = 27$ centimeters. Fit a linear model only when the scatterplot and the residual plot show a linear form, since the equation will happily produce numbers for curved data too.