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 when a straight-line model is sensible, by checking that the scatterplot has a linear form. (Guide: “From a scatterplot to a model”; Practice Q7)
- I can explain the difference between y (an observed value) and ŷ (a predicted value). (Guide: “The equation ŷ = a + bx”; Practice Q3, Q7)
- I can name the y-intercept a and the slope b in a model such as ŷ = −30.26 + 5.37x. (Guide: “Reading the slope and intercept”; Practice Q1)
- I can define interpolation and extrapolation, and say that the end points of the data interval count as interpolation. (Guide: “Interpolation and extrapolation”; Practice Q2, Q4)
Skills
- I can identify the explanatory and response variables in a context. (Practice Q5)
- I can rewrite a model using the names of the variables. (Practice Q5)
- I can calculate a predicted value by substituting x, without rounding the coefficients early. (Guide: Worked example 1; Practice Q1, Q4)
- I can use a model where x is coded, for example “years since 2000”, by substituting the coded value. (Practice Q6)
- I can decide whether a prediction is an interpolation or an extrapolation by comparing x with the smallest and largest x-values. (Guide: Worked example 1; Practice Q2, Q4, Q6)
Reasoning
- I can report a prediction in context, saying “the model predicts”, naming the variable and giving units. (Guide: Worked example 1; Practice Q5)
- I can explain why a prediction becomes less reliable the further it is extrapolated, using the context. (Guide: Worked example 2; Practice Q3, Q6)
- I can recognise an impossible prediction (for example, a negative height or time) as a sign of extrapolation or of a poor model. (Guide: Worked example 2; Practice Q6, Q7)
All ticked? Move on to Topic 5.4: Residuals, or return to the course roadmap.