Course Archives Statistical Quality Control & Operations Research Unit
Course:Applied Regression Analysis
Level: Postgraduate
Time: Currently not offered
Past Exams

Syllabus: Simple linear Regression: The simple regression model, Importance of scatterplot, Least squares method of estimation of parameters, Test for slope and intercept, Interval estimation in simple regression, Prediction of new observations, Co-efficient of determination, Estimation by maximum likelihood method.
Checking Model Adequacy: Residual analysis, Detection and treatment of outliers, Lack of fit and pure error, Need for transformation, Weighted least squares.
Multiple Linear Regression: Multiple regression models, Estimation of model parameters, Confidence intervals and hypothesis testing in multiple regression, Prediction of new observations, Multiple correlation co-efficient. Polynomial regression. Checking for the validity of model assumptions: Role of residuals and hat matrix, standardized and studentized residuals. Plots Fitted values against residuals, regressors against residuals, added variable plots, normal probability plot. Detecting influential observations: DFBETAS, DFFITS, Cooks D, COVRATIO. Sources and effects of multi-co linearity, multicolinearity diagnostics VIF and variance proportions. Methods for dealing with multicollinearity, Principal component regression and its pitfalls, Subset selection -Criteria for choice of subset size, Co-efficient of multiple determination, Residual mean square, Adjusted co-efficient of determination, Mallows Cp statistic. AIC and BIC criteria. Comparison of different criteria. Ridge regression.
Indicator Variables: Concept and use of indicator variables as regressors, models with only indicator variables, interaction teams involving indicator variables, indicator variables for segmented models.
Topics in the Use of Regression analysis: Heteroscadasticity, Transformations, Box-Cox transformation, Autocorrelation, Generalized least squares, Designed experiments for regression, Relationship between regression and analysis of variance, validation of Regression models. Non-linear models Estimation of parameters of a non-linear system.
Logistic Regression: Discrete response models. Linear probability models. Logistic regression model, Test of significance of coefficients, Multiple logistic regression model, Fitting and testing the significance of the model, Interpretation of the coefficients of the logistic regression model Dichotomous, Polytomous and Continuous independent variable, Measures of goodness of fit Pearson Chi-square and Deviance, Hosmer Lameshow tests, Logistic regression diagnostics. Probit regression.
For all the topics above: Examples and Exercises with use of software packages like Minitab / JMP/ SPSS/ Statistica/ Systat/excel etc.

Reference Texts:
1. Applied Regression Analysis(3rd Edition): By Norman R. Draper & Harry Smith, Wiley Series in Probability and Statistics, John Wiley 1998.
2. Applied Regression Analysis ( 2nd edition): By John O. Rawlings, Sastry G. Pantula & David A. Dickey, Springer 2001.
3. Introduction to Linear Regression Analysis: By D.C.Montgomery & Elizabeth A.Peck, G.Geoffrey Vining : Wiley Series in Probability & Statistics, John Wiley & Sons, 2001.
4. Regression Analysis by Example: By Samprit Chatterjee & Betram Price, Ali S Hadi, Wiley Series in Probability & Statistics, John Wiley & Sons, 2000.
5. An Introduction to Generalized Linear Models: By Annette. J. Deobson, Texts in Statistical Science, Chapman & Hall/CRC, 2002.
6. Applied Logistic Regression: By David W. Hosmer & Stanley Lemeshow, John Wiley & Sons, 2000.

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[Indian Statistical Institute]