Like the name implies, LINEar regression involves fitting a line to a set of data points. In order to fit a line, it’s helpful to understand the equation for a line, which is often written as *y=mx+b*. In this equation:

*x*and*y*represent variables, such as height and weight or hours of studying and quiz scores.*b*represents the*y-intercept*of the line. This is where the line intersects with the y-axis (a vertical line located at*x = 0*).*m*represents the slope. This controls how steep the line is. If we choose any two points on a line, the slope is the ratio between the vertical and horizontal distance between those points; this is often written as rise/run.

The following plot shows a line with the equation *y = 2x + 12*:

Note that we can also have a line with a negative slope. For example, the following plot shows the line with the equation *y = -2x + 8*:

### Instructions

**1.**

In **script.py**, we’ve again plotted `score`

(as the y-variable) against `hours_studied`

(the x-variable), with a line going through the points. Let’s see if we can improve this line so that it better fits the data. To start, the line appears to be too steep. In **script.py**, edit the equation of the line so that the slope is `10`

, then press “Run” to see the new line.

This should make the line less steep (because we are decreasing the slope). Does this fit the data better or worse?

**2.**

The line now appears to be parallel to the points but still sits below them! Leaving the slope of the line equal to `10`

, edit the equation of the line so that the y-intercept is `45`

, then press “Run” to see the new line.

This should move the line upward (because we are increasing the y-intercept). Does this new line fit the data well?