Chapter 12 Correlation

What is correlation?

When there is a clear relationship or correlation, you can show this by adding a line. This is called the line of best fit. It is also called the regression line. This term is often used when the position of the line is calculated rather than approximated. A further set of results might produce this arrangement of points. This suggests a correlation where being good at subject A means you are good at subject B. This type of relationship is called a positive correlation. A different set of results might produce this arrangement of points. Here the results form more of a line. This suggests a correlation where being good at subject A means you are not so good at subject B. This type of relationship is called a negative correlation. For these test results the points are all over the place. This means there is no correlation. That is to say, the test results for the two subjects aren’t related. Plotting each point on a graph shows the points scattered across the grid. Hence this is called a scatter graph. By looking at the points, we can see if there is a relation between the two subjects. We are looking at whether being good at one subject might mean you would be good or bad at the other. This is called the correlation. A group of students took tests in two subjects. What would it mean if the subjects were related? By putting together each person’s test results in the two subjects, we make a pair. We can plot this pair as a coordinate. The plot of all such coordinate pairs should show us whether the results are related.

Causation

This graph shows the scatter diagram of the percentage of people who smoke daily and the average life expectancy for European countries: Is it a strong or weak correlation? TOK www Does this mean that smoking causes premature death? What sort of correlation is there?

Really? Study says coffee intake has antidepressant effect on women Being left-handed makes you angry These are real headlines from newspapers across the world. Each is backed by studies that show a correlation linking the two factors together. Does this mean that one factor causes the other? www

Predictions based on regression lines

Let’s look again at the data on smoking and life expectancy: Can it be used to estimate the average life expectancy for a country in which 20% of the population smoke every day? Could it be used to estimate the average life expectancy for a country in which 60% of the population have never smoked? What about a country in which 80% of the population smoke every day?