Statistics and regression.
Analyse paired numerical data, select and assess regression models, interpret statistical claims and calculate normal probabilities.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Bivariate data and scatter plots
Keep paired measurements together and turn them into an informative scatter plot.
- 02
Direction/form/strength of association
Describe direction, shape and strength without reducing every association to one number.
- 03
Explanatory/response variables
Choose explanatory and response variables from the question being asked.
- 04
Correlation and causation
Separate an observed association from evidence for a causal explanation.
- 05
Pearson correlation and coefficient of determination
Calculate and interpret Pearson’s r and the coefficient of determination.
- 06
Least-squares regression
Fit a straight line by minimising squared vertical residuals.
- 07
Interpreting slope/intercept
Explain a fitted slope and intercept in the variables’ original units.
- 08
Outliers and justified treatment
Investigate unusual observations and justify any treatment transparently.
- 09
Residuals
Use residuals to diagnose prediction errors and the form of a fitted model.
- 10
Exponential regression
Fit and interpret exponential models using constant proportional change.
- 11
Interpolation/extrapolation
Judge whether a prediction lies within the evidence and whether the model is sensible.
- 12
Normal distributions
Use a normal model’s centre, spread and symmetry to reason about a population.
- 13
Normal probabilities and inverse-normal values
Calculate interval probabilities and work backwards from a normal percentile.
Topic review
Revisit the key ideas, then choose a practice paper.