ABSTRACT
Regression of a response on a single predictor variable is introduced with a case study of an investigation into the relation between abrasion loss of turbine blades, which is inconvenient and expensive to measure directly, and Vickers hardness measurements made at the base of the blade. The regression model is discussed and the line is fitted using the principle of least squares. The analysis continues with calculation of residuals, estimation of the standard deviation of the errors, confidence intervals for the mean value of the response given a value for the predictor. Calculations using the derived formulae are compared with MATLAB and R functions. The distinction between a designed experiment, in which values of the predictor variable are pre-selected, and an observational study in which data are a random sample from a bivariate distribution is made. Correlation analysis in the context of a random sample from a bivariate normal distribution is covered and related to the regressions. The concept of regression towards the mean is discussed. The measurement error model is introduced, with a case study of a comparison between aerial and land based surveys, and its application to estimating calibration lines is discussed. Examples of models that can be transformed into linear relationships are given. The associated experiment in Appendix E investigates the relation between descent times of paper helicopters and paper clip payload. Examples of The chapter ends with: a summary of: notation used; the main results, MATLAB and R syntax; and exercises.
