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9. Scatter Diagram Page 1

5. Scatter Diagram

Overview

A scatter diagram is a visual representation of the

relationships between selected variables.

In other words, a scatter diagram helps usdetermine whether two variables are correlated

with one another.

And when we say something is correlated… we’re

basically saying they are related to one another.

In the example to the right we see on time

delivery and customer satisfaction plotted inside of a scatter diagram… and there definitely seems to

be a rather strong positive correlation. In other words, as on time delivery increases so too doescustomer satisfaction.

Correlation Does Not Always Mean Causation

Now then, if you remember back to our first overview module of this course… we learned an

extremely important concept… namely that correlation does not automatically mean there’scausation.

The example we used that in that module was how it can be show that as the number of liquorstores increase in a neighborhood so do the number of churches built. So, one could conclude that if

a town hoped to have more churches all they need to do is build more liquor stores, right?

Of course this is complete nonsense since the two – liquor stores and churches – aren’t correlated

at all. A better explanation for this situation is that as a town grows in population there’ll be someresidents who like to visit liquor stores and some who like to attend church.

So the key point I’d like to stress here is to not get too excited when you think you’ve identifiedcorrelated variables. Instead, once we’ve identified possible correlation we should always follow the11th commandment of continuous improvement which is simply… thou shall confirm.

In other words, we need to set up an experiment as best we can in order to verify our assumption of

correlation is valid.

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R2 

While the graphical display of the scatter diagram helps us determine how much correlation exists…

there’s actually a far more accurate way to determine the level of correlation.

And this method has us examining an important statistic known as R Squared which measures the

proportion of variation explained by the model.

What this basically means is high R squared values tell us that the two variables being studied are

highly correlated.

The next logical question is how high is high. Generally speaking R squared values greater than .8

indicate strong correlation while R Squared values between .5 and .8 generally indicate moderatecorrelation. Finally, when see R Squared values less than .5 it’s safe to say that little to no correlationexists within this particular study.

Building Predictive Models

Scatter diagrams can help us build predictive models. By using statistical software such as Sigma XLwe are presented with a formula as shown below. If our model is adequate, meaning R squared is at

least 0.80 we can leverage the formula to build predictive equations as shown in the example below.