Contents
1 Introduction
1.1 Scatter plot
1.2 Statistical and deterministic relationships
1.3 What “linear” means
1.4 Uses of regression
1.5 Steps in a regression analysis
2 Simple linear regression
2.1 The model and its assumptions
2.2 Least-squares estimation of the parameters
2.3 Properties of the fitted line
2.4 Properties of the least-squares estimators
2.5 Estimation of \(\sigma ^2\)
2.6 Maximum likelihood estimation
2.7 Sampling distributions under normality
2.8 Hypothesis tests on the slope and intercept
2.9 Analysis of variance
2.10 The coefficient of determination
2.11 Interval estimation
2.12 Correlation
2.13 Practice problems
3 Multiple linear regression
3.1 Matrix results we shall need
3.2 The model in matrix form
3.3 Least-squares estimation
3.4 Fitted values, residuals and the hat matrix
3.5 Properties of the least-squares estimator
3.6 Estimation of \(\sigma ^2\) in multiple regression
3.7 Distribution theory under normality
3.8 Test for significance of regression
3.9 \(R^2\) and adjusted \(R^2\)
3.10 Tests on individual coefficients
3.11 The extra-sum-of-squares principle
3.12 Confidence and prediction intervals
3.13 Practice problems
4 Model adequacy checking
4.1 Residuals and their properties
4.2 Scaled residuals
4.3 Residual plots
4.4 Outliers
4.5 The PRESS statistic
4.6 Lack of fit and pure error
4.7 Practice problems
5 Test for influential observations
5.1 Leverage
5.2 Cook’s distance
5.3 DFFITS and DFBETAS
5.4 The effect on precision: COVRATIO
5.5 Applying the measures
5.6 What to do about influential observations
5.7 Practice problems
6 Transformation & weighting to correct model inadequacies
6.1 Variance-stabilizing transformations
6.2 Transformations to linearize the model
6.3 The Box–Cox method
6.4 Weighted least squares
6.5 Practice problems
7 Selecting the Best Regression Model
7.1 The cost of leaving regressors out, and of putting them in
7.2 Criteria for comparing models
7.3 All possible regressions
7.4 Stepwise methods
7.5 Cautions in model selection
7.6 Practice problems
8 Multicollinearity
8.1 The correlation form of the model
8.2 Effects of multicollinearity
8.3 Diagnostics
8.4 Remedies
8.5 Practice problems
9 Dummy variables
9.1 A qualitative regressor with two levels
9.2 Fitting and testing
9.3 Factors with more than two levels
9.4 Piecewise linear regression
9.5 Practice problems
10 Polynomial regression
10.1 Polynomial models in one variable
10.2 Orthogonal polynomials
10.3 Piecewise polynomials: splines
10.4 Polynomial models in two or more variables
10.5 Nonparametric regression
10.6 Practice problems
11 Generalized linear models
11.1 Binary responses and the logistic model
11.2 Maximum likelihood estimation
11.3 Inference in logistic regression
11.4 The exponential family and generalized linear models
11.5 Poisson regression
11.6 Practice problems
12 Non linear estimation
12.1 Non-linear models
12.2 Least squares and the normal equations
12.3 The Gauss–Newton method
12.4 Inference
12.5 Conditionally linear parameters
12.6 Practice problems
13 Regression models with autocorrelated errors
13.1 Sources and effects of autocorrelation
13.2 Detecting autocorrelation
13.3 Estimating the parameters
13.4 Forecasting
13.5 Practice problems
14 Measurement errors & calibration problem
14.1 Errors in the variables
14.2 The calibration problem
14.3 Practice problems
References
References