Online College Courses for Credit

Walk the Line:  Linear Correlation

Walk the Line: Linear Correlation

Author: Nate Muckley

Learn about linear correlation and it's relation to statistics. This also has a tutorial about making scatter plots and finding r in Microsoft Excel!

Learn about the principles of Linear Correlation in slideshows and words. Then learn how to make scatter plots and find the coefficient of linear correlation. Plus an appearance from Math Man!

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

Begin Free Trial
No credit card required

47 Sophia partners guarantee credit transfer.

299 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 33 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


What is Linear Correlation?

   Let's look at this graph:


See how the dots appear random? This is said to have no correlation.

Here's another graph:


There is a sort of pattern.  Except for an outlier or two, the data seems to be generally creating a line going up.  There is some positive correlation.

And lastly, look here:

On this graph, the points clearly form a   straight line.  It has perfect positive correlation.

     I hope you've been able to get the gist of "Linear Correlation" without seeing an exact definition.  But in case you didn't, Linear Correlation is the strength of the line-pattern that the data points fall on--the more like a line, the stronger the correlation.

     Linear Correlation is a solid idea for what is generally displayed on the scatterplot: "the direction, form, and strength of the relationship between two quantitative variables" (Yates).

This packet will show you all about linear correlation, and how to use Microsoft Excel to make a scatterplot & find the coefficient of linear correlation of you own.



Source: Yates, Moore, McCabe. "The Practice of Statistics" W H. Freeman and Company, 1999


For this packet, we will use the following data:

     A math class of ten people took a quiz.  On the quiz, each student wrote how many hours that week they had studied for the quiz.  The teacher collected the following data:

Student:                  Score (out of 20):                  Hours studying:

                     A)                                    20                                         5

                     B)                                     19                                        4.5

                     C)                                     17                                         1

                     D)                                     17                                         4

                     E)                                     15                                         4

                     F)                                     14                                         3

                     G)                                    13                                         2.5

                     H)                                    13                                          2

                     I)                                     11                                         .5

                     J)                                     6                                          0


Watch & learn.

Using Microsoft Excel

I used Microsoft Excel 2008 on a Mac, but the process should be pretty much the same for all versions of Excel.

Math Man says:

Source: Math Man made with the help of Hero Machine at