Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain that the least-squares line is the line with the smallest possible sum of squared residuals, and why the residuals are squared. (Guide: “Which line is the best line?”; Practice Q6)
- I can explain why a line whose residuals add to 0 is not necessarily the least-squares line. (Guide: “Facts about the least-squares line”; Practice Q6)
- I can explain that the slope and intercept are statistics from one sample and would change with a different sample. (Guide: “Facts about the least-squares line”)
- I can explain why b and r always have the same sign. (Guide: “Background: how the slope is linked to r”; Practice Q2)
Skills
- I can use technology to find a, b, r and r², with the explanatory variable entered as x. (Guide: Worked example 1; Practice Q4)
- I can read the slope, intercept and r² from technology output and write the equation with the variables defined. (Guide: Worked example 2; Practice Q5)
- I can use the fact that the line passes through (x̄, ȳ) to find ȳ or the intercept. (Guide: Worked example 2; Practice Q3, Q5)
- I can find r from r², choosing the sign from the slope. (Guide: “The coefficient of determination, r²”; Practice Q2, Q7)
- I can make a prediction with the line and say whether it is interpolation or extrapolation. (Guide: Worked example 1; Practice Q4)
Reasoning
- I can interpret the slope in context as a predicted change in y per one-unit increase in x, with units. (Guide: “Interpreting the slope and the y-intercept”; Practice Q1, Q4)
- I can interpret the y-intercept in context, or explain why it has no sensible meaning. (Guide: Worked example 2; Practice Q5)
- I can interpret r² as the proportion of the variation in y explained by the linear relationship with x. (Guide: Worked example 1; Practice Q5, Q7)
- I can spot wrong claims about r², extrapolation and causation made from a regression line. (Practice Q7)
All ticked? This is the last topic of the course. Go back to the Topic 5.4 residuals study guide to practise checking a line, or return to the course roadmap to review earlier units.