Walk the Line: 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.

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