Scatterplots A way of displaying numeric data

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Presentation transcript:

Scatterplots A way of displaying numeric data Used to show the relationship between two variable Quantities displayed may be directly related but may not be Used to make predictions based on trends in data

Things to remember If one variable depends on the other (either obviously or you have good reason to think it does) then the dependent variable goes on the vertical axis The scales on each axis do not need to be the same and they do not need to start at 0 Label, label, label your axes and give units (if possible)

Exercise #1 Using a piece of graph paper, make a scatter plot of the following set of data, making sure to label the axes properly and also making sure to label the scale on each axis.

Exercise #1 Key

Correlation Coefficient Most commonly used measure is called Pearson’s correlation coefficient A numeric way of evaluating whether or not two variables are related Number ranges from –1 to 1 depending on the strength of the correlation Measures how well a linear equation fits the data*

Correlation Coefficient Positive correlation indicates a linear equation with a positive slope is a good fit Negative correlation indicates a linear equation with a negative slope is a good fit The closer to 1 (or –1), the better a linear equation fits the data

Perfect Positive Correlation (r = 1)

Perfect negative correlation (r = –1)

No correlation (r = 0)

Strong Positive Correlation (r = 0.65)

Danger! You have to look at the data – all of these have a correlation coefficient of 0.81!

Example of Bivariate Data with a strong positive correlation

Bivariate data with a strong negative correlation

Another example of positive correlation.