Bivariate Statistics — Objectives | Mathematics Department

Scatter 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.

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.

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.