# 3: Linear Regression

- Page ID
- 7797

Quick review of equations for lines:

Recall the equation of a line is usually in the form \(y = mx + b\), where \(x\) and \(y\) are variables and m and b are numbers. Some basic facts about lines:

- If you are given a number for x, you can plug it in to the equation \(y=mx+b\) to get a number for \(y\), which together give you a point with coordinates (x, y) that is on the line.
- m is the
*slope*, which tells how much the line goes up (increasing y) for every unit you move over to the right (increasing x) – we often say that the value of the slope is \(\ m=\frac{rise}{run}\).*positive*, if the line is tilted up,*negative*, if the line is tilted down,*zero*, if the line is horizontal, and*undefined*, if the line is vertical.

- You can calculate the slope by finding the coordinates (x
_{1}, y_{1}) and (x_{2}, y_{2}) of any y_{2}−y_{1}two points on the line and then \(\ m = \frac{y_2 - y_1}{x_2 - x_1}\). - In particular, x
_{2}−x_{1}=1,then \(\ m =\frac{y_2 - y_1}{1} = y_2 - y_1\) - so if you look at how much the line goes up in each step of one unit to the right, that number will be the slope m (and if it goes*down*, the slope m will simply be negative). In other words, the slope answers the question “for each step to the right, how much does the line increase (or decrease)?” - b is the y
*-intercept*, which tells the y-coordinate of the point where the line crosses the y-axis. Another way of saying that is that b is the y value of the line when the x is 0.