Study Notes
Correlation and regression involve analyzing the relationship between two variables using scatter diagrams and linear regression techniques. The product moment correlation coefficient measures the strength and direction of a linear relationship.
- Scatter Diagram — a graph that shows the relationship between two variables using points. Example: A scatter diagram can show how breath rate affects pulse rate.
- Independent Variable — a variable that is controlled or set by the researcher, plotted on the x-axis. Example: Breath rate in an experiment.
- Dependent Variable — a variable that is measured and depends on the independent variable, plotted on the y-axis. Example: Pulse rate in an experiment.
- Correlation — describes the strength and direction of a linear relationship between two variables. Example: Positive correlation means both variables increase together.
- Linear Regression — a method to model the relationship between two variables by fitting a line. Example: The line of best fit in a scatter diagram.
- Least Squares Regression Line — a line that minimizes the sum of the squares of the vertical distances of each data point from the line. Example: Used to predict values of the dependent variable.
- Product Moment Correlation Coefficient (PMCC) — a measure of the linear correlation between two variables, ranging from -1 to 1. Example: An r value of 0.8 indicates a strong positive correlation.
Exam Tips
Key Definitions to Remember
- Scatter Diagram
- Independent Variable
- Dependent Variable
- Correlation
- Linear Regression
- Least Squares Regression Line
- Product Moment Correlation Coefficient (PMCC)
Common Confusions
- Confusing independent and dependent variables
- Misinterpreting the PMCC value as causation
Typical Exam Questions
- What is a scatter diagram? A graph that shows the relationship between two variables using points.
- How do you interpret a positive correlation? Both variables increase together.
- What does a PMCC of 0 indicate? No linear correlation between the variables.
What Examiners Usually Test
- Ability to draw and interpret scatter diagrams
- Understanding of how to calculate and interpret the least squares regression line
- Calculation and interpretation of the product moment correlation coefficient