Mathematics: Applications and Interpretation HL

Technology, diagnostics, and model choice

Technology output, residual diagnostics, regression interpretation, numerical solving, and model-choice reasoning for AI HL.

Interpret residual plots Use residual size and sign to judge prediction error and model suitability. Interpret coefficient of determination Interpret \(r^2\) as the proportion of variation explained by a regression model. Model exponential decay and half-life Use exponential decay parameters to calculate half-life or remaining amount. Interpret logarithmic regression parameters Use logarithmic regression output to predict or interpret a model parameter. Use power regression models Use a power regression equation to calculate a contextual prediction. Evaluate piecewise models Choose the correct branch of a piecewise model before calculating the value. Calculate covariance from summaries Use paired-data summaries to calculate covariance and interpret its sign. Interpret regression slope and intercept Connect regression coefficients to contextual prediction and rate meaning. Judge extrapolation from regression models Decide whether a prediction lies inside or outside the data domain. Use moving averages in time series Calculate a moving average and interpret smoothing in a time series. Calculate correlation from covariance Use covariance and standard deviations to calculate a correlation coefficient. Use seasonal indices in time series Deseasonalise or reseasonalise time-series values using seasonal indices. Calculate standard deviation from summaries Use summary totals to calculate sample standard deviation. Use Spearman rank differences Calculate Spearman rank correlation from squared rank differences. Interpret residual standard deviation Interpret the residual standard deviation as typical prediction error.