Correlation and regression
Use scatter, correlation and directional least-squares fits to make contextual predictions and recognise their limits.
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Before you begin
Use scatter, correlation and directional least-squares fits to make contextual predictions and recognise their limits.
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
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. Exclude derivation of formulae, r² = b₁b₂ for regression coefficients, hypothesis tests and transformations to achieve linearity.
- 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. Exclude derivation of formulae, r² = b₁b₂ for regression coefficients, hypothesis tests and transformations to achieve linearity.
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Correlation, regression and prediction
Interpret scatter and residuals, fit each prediction direction, and assess range, outliers and causal claims.