Topic 3: Statistical Models

3 dot points, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

How do we measure the strength and direction of a relationship between two variables?

Display bivariate data in a scatterplot and describe the association using form, direction, strength and the correlation coefficient r.

How to read a scatterplot for form, direction and strength, interpret the correlation coefficient r and r squared, and avoid concluding causation from correlation.

7 min read →

How do we describe and compare values within a bell-shaped distribution?

Use the normal distribution, the 68-95-99.7 rule and z-scores to describe data and compare values from different distributions.

How to apply the 68-95-99.7 rule, calculate z-scores to standardise values, find proportions and compare results from different normal distributions.

8 min read →

How do we fit the best straight line to data and use it to predict?

Determine and interpret the least-squares regression line, use it to make predictions, and assess fit using residuals.

How to find and interpret the least-squares line y = a + bx, use it for prediction, distinguish interpolation from extrapolation, and read residuals to judge the fit.

8 min read →