Least-squares regression line

The least-squares regression line is the best-fit line for predicting the response from the explanatory variable, chosen to minimize the total squared vertical distance from the points. Its equation is $\hat{y} = a + bx$, where $\hat{y}$ (read y-hat) is the predicted response, $a$ is the y-intercept, and $b$ is the slope. For example, $\hat{y} = 50 + 5x$ predicts a score of 75 when $x = 5$ hours of study. The line always passes through the point of averages $(\bar{x}, \bar{y})$.