A regression is a process that takes all the points and calculates the equation that best 'fits' those points. A linear regression simply means that the equation will be the equation of a line. Although a linear regression can be quite helpful in understanding data, it can sometimes be misleading, as Anscombe's Quartet shows.

### How to Calculate A Linear Regression

### Examples of Linear Regressions and Graphs

In both cases, the line of best fit is the y = x. As you can see from both graphs, this equation is a better fit for the first set of points but it still fits the 2nd set pretty well.

#### 1^{st} set of points

#### 2^{nd} Set of points

### Practice Problems

The linear regression that best fits these points is the equation

y = ¼x +7.75

Now, using this equation what is the y value when x = 54?

Substitute x = 54 into the linear regression equation that you just found

y = ¼x + 7.5

y = ¼(54) + 7.5

y = 21

The linear regression that best fits these points is the equation

y = 1.08x − 2125

Now, using this equation what is the y value when x = 2010?

Substitute x = 2010 into the linear regression equation that you just found

y = 1.08(x) − 2125

y = 1.08(2010) − 2125

y = 55