TABLE OF CONTENTS The techniques discussed in this chapter belong to a group of methods known as regression analysis, which is probably the most frequently used of all data analysis approaches. This chapter was concerned in particular with linear regression, in which the model equation relates a dependent variable to a sum of model terms called regressors, and each regressor is multiplied by an unknown constant parameter to be determined from measured data. The main topics covered were linear regression, model structure determination, and data collinearity.
Details were given for the calculations required to estimate unknown parameters in a linear regression model using the least-squares principle. The resulting parameter estimates are unbiased, efficient, and consistent. The calculations also provide standard errors of the estimated parameters as a measure of their accuracy, along with measures of the quality of the model fit to the data, such as fit error and the coefficient of determination. By assuming a normal distribution for measurement errors, it was possible to construct confidence intervals for the estimated parameters, estimated output, and predicted output.
Least-squares parameter estimation using linear regression assumes that the form of the model is known. In practice, however, it is often unclear what terms should be included in the model. This uncertainty may result in a reduced model or in a model with too many terms, neither of which will be a good predictor for other similar data. Therefore, there is a need to find an adequate model that...
