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.
- Simple and Multiple linear regressions: Least squares fit, Properties and examples. Polynomial regression: Use of orthogonal polynomials. Analysis of multiple regression models, estimation and testing of regression parameters, sub-hypothesis testing, restricted estimation.
- Selection of variables, adequacy and validation of models. Use of dummy variables, regression with ordinal data. Introduction to non-parametric regression. Logistic regression.
- Regression diagnostics - non-normal errors, non-constant error variances, non independent observations, influential observations (outliers), non-linearity of the model, multicollinearity in the data. Remedial measures - regression under non-normal errors, transformation of data, generalized least-squares, robust regression, ridge regression, Regression using principal components. Model over-fitting, model under-fitting.
Multiple regression fitting with three and four independent variables; Estimation of residuals, their applications in outlier detection, distribution of residuals; Test of homoscedasticity, and normality, Box-Cox transformation; Restricted estimation of parameters in the model, hypothesis testing, Step wise regression analysis; Least median of squares norm, Orthogonal polynomial fitting.