Quick Summary
- Correlation describes the relationship between two quantities: positive, negative, or none (zero).
- Scatter graphs plot paired data as crosses (×) — never joined up — so you can see the pattern.
- "Correlation does not imply causation" — just because two things move together doesn't mean one causes the other.
- A line of best fit is drawn by eye through the mean point (x̄, ȳ) to summarise a linear trend.
- Interpolation (predicting inside your data range) is reliable; extrapolation (predicting outside it) is risky.
- A linear regression line (y = mx + b) is the calculator-generated "ideal" version of a line of best fit, and it always passes through the mean point too.
1. Correlation — What's the Relationship?
Imagine you're comparing two things about a group of people — say, their height and their shoe size. As one goes up, does the other tend to go up too? Go down? Or is there no obvious link at all? That relationship is what correlation measures.
There are three types, and you need to be able to spot each one just by looking at the shape a set of dots makes.
Positive Correlation
This is when both quantities increase together. As one goes up, so does the other. Think: as temperature rises, ice cream sales rise. On a graph, the dots drift from the bottom-left up to the top-right — like climbing a hill. This gives the line of best fit a positive gradient.
y
| ×
| ×
| × ×
| ×
| ×
| ×
|×
+------------------------- x
Positive correlation: as x increases, y increases too — dots rise left to right
Negative Correlation
This is the opposite: as one quantity increases, the other decreases. Think: as a car gets older, its resale value drops. On the graph, dots run from top-left down to bottom-right, giving a negative gradient.
y
|×
| ×
| × ×
| ×
| ×
| ×
| ×
+------------------------- x
Negative correlation: as x increases, y decreases — dots fall left to right
No (Zero) Correlation
Here, there's no pattern at all — the dots are scattered randomly, like a "cloud." Think: the mass of snails and people's exam scores — completely unrelated. There's no sensible straight line you could draw through it.
y
| × ×
| × ×
| × ×
| × ×
|× ×
| ×
+------------------------- x
No correlation: dots form a random cloud with no clear direction
Strength matters too
Correlation isn't just "positive/negative/none" — it can also be weak or strong. The rule is simple: the closer the dots huddle to a straight line, the stronger the correlation. If they're tightly packed along an imaginary line, that's strong. If they're loosely scattered but still trending in a direction, that's weak.
"Correlation Does Not Imply Causation"
positive correlation
What to Memorise