Unit I

Simple linear regression: Examples of simple linear regression; Interpretation of parameters; Estimation of the slope and the intercept in simple linear regression; Sampling properties of estimates. Theory of point estimation: least squares, maximum likelihood, method of moments; Confidence Intervals for parameters in simple linear regression.

Unit II

Multiple linear regression: Design matrix; Interpretation and estimation of parameters; Multicollinearity; Hypothesis tests: t-test, F-test, Likelihood-ratio test; Weighted least-squares.

Unit III

Residuals and their analysis: Assessing goodness-of-fit, normality, homogeneity of variances, detection of outliers and influential observations; Diagnostic plots for linear regression models.

Unit IV

Model selection: Mallow’s Cp, AIC, BIC, R-squared, subset selection of independent variables, transformation of dependent and independent variables, multicollinearity, principal component regression, ridge-regression, Lasso.

Unit V

Logistic Regression: Statistical models for binary data; Interpretation of odds and odds ratios; Maximum likelihood estimation in logistic regression; Deviance, Residual analysis for logistic regression.

CO1: Apply simple linear regression model to real life examples.
CO2: Understand multiple linear regression models with applications and concept of Multicollinearity and autocorrelation.
CO3: Compute multiple and partial correlation and checking residual diagnostic to validate model.
CO4: Apply Logistic and Non-linear regression models and its implementation in real life situation.

1. G. Seber and A. Lee “Linear Regression Analysis”, SecondEdition, Wiley, 2003.
2. A. Dobson and A. Barnett, “An Introduction to Generalized Linear Models”, Third Edition, Chapman and Hall/CRC, 2008.
3. N. Draper and H. Smith,“Applied Regression Analysis”, Third Edition, Wiley, 1998.
4. J. Fox, “ Applied Regression Analysis, Linear Models and Related Methods”, Sage, 1997.
5. C. Rao and H. Toutenburg, “Linear Models: Least Squares and Alternatives”, Second Edition, Springer, 1999.