﻿ Linear Regressions. How to calculate linear regressions and analyze the results

# Linear Regressions

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.

### 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.

#### 1st set of points #### 2nd Set of points ### Practice Problems

Step 1

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

Step 1

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

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