The notion of prediction

Causal relationships
If one variable, X, is thought to directly affect the other, Y, we might hope to predict the value of Y if the value of X is changed.
Non-causal relationships
Even if the relationship is not causal, we are often still interested in predicting the value of one variable from a known value of the other variable.

Notation and convention

If the variables can be classified as an explanatory variable and a response, we use the letter X to denote the explanatory variable and Y to denote the response.

Always draw the response variable, Y, on the vertical axis of a scatterplot and X on the horizontal axis.

Predicting the response

The correlation coefficient describes the strength of a relationship, but does not help you to predict Y from X.

A curve or straight line that is drawn close to the crosses on a scatterplot (by eye or by any other method) is called a regression line and can be used to 'read off' the y-value corresponding to any x.