Bivariate Statistics
Term 3
Scatter plots · Correlation · Line of best fit · Regression
Learning Objectives
PrintScatter Plots and Correlation
- 1. Identify the independent (explanatory) variable and the dependent (response) variable in a bivariate context.
- 2. Construct a scatter plot from a bivariate data set, with appropriate scales and labels.
- 3. Describe the form (linear / non-linear), direction (positive / negative) and strength (weak / moderate / strong) of a relationship.
- 4. Distinguish between correlation and causation, and identify possible confounding variables.
- 5. Interpret Pearson's correlation coefficient $r$ as a measure of the strength and direction of a linear relationship.
Line of Best Fit
- 6. Draw a line of best fit by eye through the mean point of the data.
- 7. Use technology (GDC or spreadsheet) to find the equation of the least-squares regression line $y = mx + c$.
- 8. Interpret the gradient and $y$-intercept of the regression line in the context of the data.
- 9. Use the regression equation to make predictions (interpolation), and discuss the danger of extrapolation.
Residuals and Goodness of Fit (Extended)
- 10. Calculate the residual for a data point as $\text{observed} - \text{predicted}$.
- 11. Interpret the coefficient of determination $r^2$ as the proportion of variation explained by the model.
- 12. Compare $r$ and $r^2$ for different bivariate data sets and discuss which model fits best.
- 13. Discuss the limitations of a linear model when residuals show a clear pattern.
Assessments
Bivariate statistics end-of-unit test
Criterion A
60 min
Test on drawing scatter plots, describing correlation, fitting a line of best fit by hand and by regression, and using the line to make and critique predictions.
Review Pack
Open review hub
Fluency Pack A — 40 questions
Fluency Pack B — 40 questions
Problem-solving — 12 unfamiliar tasks
Worked solutions (Pack A + B + problems)