Correlation & Regression
Bivariate data is data with two variables, and can be represented in a scatter diagram. We can describe the correlation between the two variables based on how much of a straight line the points on the diagram form.
Correlation describes the nature of the linear relationship between two variables.
A negative correlation occurs when one variable increases as the other decreases.
A positive correlation occurs when both variables increase together.
The relationship can be described as causal if a change in one variable induces a change in the other. It is vital to remember that just because there may be a correlation, no matter how strong, between two variables, it does not mean the relationship is causal.
Correlation does not imply causation
You need to consider the context of the variables and use common sense to decide whether or not there is causation as well as correlation.
The product moment coefficient, r, is a measure of strength for linear correlation between two variables. It takes values from -1 to 1, where
If r = 1 the correlation is perfect and positive
If r = 0 there is no correlation at all
If r = -1 the correlation is perfect and negative
You calculate the product moment coefficient using a stats-equipped scientific calculator.
On a CASIO ClassWiz fx-991EX, to calculate the product moment coefficient, r:
Click 6: statistics
Click 2: y=a+bx
Input your data in the table
Click 3: Regression Calc
r is the product moment coefficient