About this topic
Before you begin
Use directional least-squares fits and square, reciprocal or log transformations, then assess predictions in their original setting.
Learning goals
- Fit and interpret correlation and regression models
- Calculate product-moment correlation from specified paired data
- Calculate complete ordered intercept and gradient from specified paired data
- Calculate original-response model prediction from specified paired data
- Calculate signed residual on the fitted response scale from specified paired data
- Calculate sum of squared residuals on the fitted response scale from specified paired data
- Calculate original-input solution of a specified fitted calibration model from specified paired data
- Calculate product-moment correlation from specified paired data and transformations
- Calculate complete ordered intercept and gradient from specified paired data and transformations
- Calculate original-response model prediction from specified paired data and transformations
- Calculate signed residual on the fitted response scale from specified paired data and transformations
- Calculate sum of squared residuals on the fitted response scale from specified paired data and transformations
- Calculate original-input solution of a specified fitted calibration model from specified paired data and transformations
Syllabus statements covered
- Include: scatter diagrams and plausibility of a linear relationship; correlation coefficient as a measure of fit; interpretation of product moment correlation near −1, 0 and 1; linear regression and least squares; interpolation and extrapolation; appropriate regression line for prediction or estimation in practical situations, including how well it models the situation. Include square, reciprocal or logarithmic transformations to achieve linearity. Exclude derivation of formulae, r² = b₁b₂ for regression coefficients, hypothesis tests.
- Include: scatter diagrams and plausibility of a linear relationship; correlation coefficient as a measure of fit; interpretation of product moment correlation near −1, 0 and 1; linear regression and least squares; interpolation and extrapolation; appropriate regression line for prediction or estimation in practical situations, including how well it models the situation. Include square, reciprocal or logarithmic transformations to achieve linearity. Exclude derivation of formulae, r² = b₁b₂ for regression coefficients, hypothesis tests.
Choose a lesson
Work through them in order.
- Not startedCorrelation, regression and predictionNextInterpret scatter and residuals, fit each prediction direction, and assess range, outliers and causal claims.
- Not startedTransformed regression and original scalesNextFit square, reciprocal and logarithmic models, recover predictions and compare errors on their stated scales.