**DESCRIPTION OF COURSES**

**AS 603 REGRESSION ANALYSIS (1L+1P)**

**Objective**

This course is meant to prepare the students in linear and non-linear regression methods useful for statistical data analysis. They would also be provided a mathematical foundation behind these techniques and their applications in agricultural data.

**Theory**

UNIT I

Simple and multiple linear regressions: Least squares fit, properties and examples. Polynomial regression: analysis of multiple regression models, estimation and testing of regression parameters, sub-hypothesis testing, restricted estimation. Use of orthogonal polynomials and their fitting.

UNIT II

Regression diagnostics: overview, non-normal errors, non-constant error variances and correlated observations, nonlinearity of the model. Distribution of residuals. Test of homoscedasticity and normality. Influential observations and outliers. Multicollinearity. Transformation of data. GLS. Ridge regression, principal component regression and robust regression.

UNIT III

Model over-fitting and under-fitting, selection of variables, step-wise regression analysis. Adequacy and validation of models. Indicator variable technique. Regression with ordinal data. Non-linear regression models. Non-parametric regression.

**Practicals**

Fitting of simple and multiple linear regressions, polynomial regression. Sub-hypothesis testing, restricted estimation. Fitting of orthogonal polynomials. Test for non-linearity of the model, test of homoscedasticity, test for normality, tests for influential observations and outliers. Multicollinearity: detection, ridge regression and principal component regression. Robust regression. Model over-fitting and under-fitting. Selection of variables, step-wise regression analysis. Adequacy and validation of models, Indicator variable technique. Fitting regression with ordinal data. Fitting of non-linear regression models and Non-parametric regression.

**Suggested Readings**

- Barnett, V. and Lewis, T. 1984.
*Outliers in Statistical Data*. John Wiley. - Belsley, D.A., Kuh, E. and Welsch, R.E. 2004.
*Regression Diagnostics-Identifying Influential Data and Sources of Collinearity*. John Wiley. - Chatterjee, S., Hadi, A. and Price, B. 1999.
*Regression Analysis by Examples*. John Wiley. - Draper, N. R. and Smith, H. 1998.
*Applied Regression Analysis*. John Wiley. - Kleinbaum, D.G. and Kupper, L.L. 1978.
*Applied Regression analysis and other Multivariate Methods*. Massachusetts: Duxbury Press. - McCullagh, P. and Nelder, J.A. 1999.
*Generalized Linear Models*. Chapman and Hall. - Montgomery, D.C., Peck, E. and Vining, G. 2003
*. Introduction to Linear Regression Analysis*. John Wiley. - Rao, C.R. 1973.
*Linear Statistical Inference and its Applications*. John Wiley.