Regression and Correlation
Linear regression fits a line $y=a+bx$ to paired data for estimation and prediction.
$$b=\frac{\sum (x-\bar{x})(y-\bar{y})}{\sum (x-\bar{x})^2}, \qquad a=\bar{y}-b\bar{x}$$
Linear regression fits a line $y=a+bx$ to paired data for estimation and prediction.
Fit a line to points $(1,2)$, $(2,5)$, and $(3,7)$. Estimate $y$ when $x=4$.
Using least squares, $\bar{x}=2$ and $\bar{y}=14/3$.
At $x=4$, $y=9.67$.