Main topics (Detailed topics ) |
Multiple linear regression
Multiple regression models, General linear regression model in matrix terms, Least squares estimators, Analysis of variance results, Inferences about regression parameters, Inferences about mean response, Predictions of new observations, Decomposition of SSR into extra sums of squares, Coefficients of partial determination, Testing hypotheses concerning regression coefficients in, Matrix formulation of general linear test,
Residual analysis
Residuals, Graphic analysis of residuals, F test for lack of fit, Remedial measures,
Polynomial regression
Polynomial regression models, Estimating the maximum or minimum of a quadratic regression function, Some further comments on polynomial regression.
Indicator variables
One independent qualitative variable, Model containing interaction effects, More complex models, Other uses of independent indicator variables. Some considerations in using independent indicator variables. Dependent indicator variable. Linear regression with dependent indicator variable, Logistic response function.
Model building and variable selection
Selection of independent variables, Nature of the problem, All possible regression models, Stepwise regression, Implementation of selection procedures.
Influential data
Multicollinearity, influential observations, and other topics in regression analysis, Reparameterization to improve computational accuracy, Problems of multicollinearity, Variance inflation factors and other methods of detecting
multicollinearity.
Ridge regression
Ridge regression and other remedial measures for multicollinearity, Identification of outlying observations, Identification of influential observations and remedial measures.
Nonlinear regression
Linear, intrinsically linear, and nonlinear regression models, Least squares estimation in nonlinear regression, Inferences about nonlinear regression parameters. |