Interpreting trends and their strength
In the exam, you need to be able to spot the general trend of a graph and, sometimes, understand how strong that trend actually is.
Paper 1 and Paper 2 both use a lot of graphs
Paper 1 and Paper 2 both include a lot of graphs to show trends in human behaviour, natural changes or other changes in the world.
It is also possible that the IB not only asks you to spot the general trend of a graph, but also to understand and interpret the actual strength of that trend.
To do that in the exam, you need to know two things:
Direction + strength of a linear relationship.
How much of the variation is explained by the fitted model.
Correlation coefficient, r
Direction and strength of a linear relationship.
How it works
The correlation coefficient tells you whether two variables move together in a positive or negative direction, and how strong that relationship is.
Margarine consumption & divorce in Maine
From 2000-2009, these two completely unrelated variables had an extremely strong positive correlation of about r = +0.993.
That does not mean margarine causes divorce. Both variables simply changed in a very similar way over time.
The sign of r tells you the direction
As X increases, Y tends to increase.
r > 0
As X increases, Y tends to decrease.
r < 0
r tells you two things: the sign gives you the direction, and how close r is to +1 or -1 gives you the strength.
How close are the points to the trendline?
Move the slider. The closer the points are to the grey trendline, the stronger the correlation.
Positive r = both variables generally increase together. Negative r = one generally decreases as the other increases.
Coefficient of determination, R²
How much of the variation the model actually explains.
What is the difference between r and R²?
Direction + strength.
r = -0.80 → strong negative linear correlation.
How much variation the model explains.
R² = 0.64 → 64% of the variation in Y is explained by the model.
R² = r². So if r = -0.80, then R² = 0.64.
Because r is squared, R² does not tell you whether the relationship is positive or negative.
Higher R² = the model explains more of the variation
Move the slider and watch how tightly the data fit the grey trendline.
Putting it together
Write r and R² as exam sentences, then practise on your own.
Turn the number into one sentence
Interpret r and R²
Common mistakes
r = 0.8 does not mean 80% is explained.
Use the graph or sign of r for positive vs negative.
Strong correlation does not prove one variable caused the other.