Edexcel International A Level
Statistics 1 (YMA01)
Correlation & Regression
Complete revision guide with interactive charts for bivariate data analysis, scatter diagrams, correlation measurement, linear regression, and coded transformations
What Does Bivariate Data Mean?
Bivariate Data: Data collected on two variables that looks at how one of the factors affects the other. Each data value from one variable is paired with a data value from the other variable.
✓ Key Points About Bivariate Data:
- A lot of statistics is about looking at how different factors, or variables, change how data behaves
- The two variables are often related, but do not have to be
- Each value is paired with a corresponding value from the other variable
What is a Scatter Diagram?
Scatter Diagram: A way of graphing bivariate data where points represent pairs of values, with one variable on the x-axis and the other on the y-axis.
📊 Example: Question Packs Completed vs Exam Score
Plotting Scatter Diagrams
Key Elements of a Scatter Diagram
Independent (Explanatory) Variable: The variable that can be controlled in the data collection. This is plotted on the x-axis.
Dependent (Response) Variable: The variable that is measured or discovered in the data collection. This is plotted on the y-axis.
Why This Matters: The variable you think might cause changes goes on the x-axis (independent). The result or outcome goes on the y-axis (dependent).
💡 Examiner Tip: You may be asked to plot points, or add to an existing scatter diagram. Always check the scales carefully when plotting any points.
Using Scatter Diagrams to Find Relationships
✓ What Scatter Diagrams Show:
- Scatter diagrams allow statisticians to look for relationships between the two variables
- Some scatter diagrams will show a clear relationship known as correlation
- Others will not display an obvious relationship
- If a scatter diagram shows a relationship, you may be asked to identify outliers
Identifying Outliers
Outlier: A data point that does not fit the general pattern seen on the graph. Points that lie significantly away from the general trend are outliers.
⚠ About Outliers:
- There will likely be a maximum of one or two outliers on any scatter diagram
- They may represent unusual circumstances or data collection errors
- Can significantly affect correlation values and regression lines
What is Correlation?
Correlation: How the relationship between the two variables is described. It shows the strength and direction of a linear relationship.
Types of Linear Correlation
✓ Understanding Correlation Types:
- Perfect Linear Correlation: The bivariate data will all lie on a straight line on a scatter diagram
- Positive Correlation: Both variables are increasing together
- Negative Correlation: One variable is increasing while the other is decreasing
- Strong vs Weak: