MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 7: Simple Linear Regression, Symmetric Matrix, Bias Of An Estimator

• School: Indian Institute of Technology - IIT Kanpur
• Department: Mathematics
• Course: MTH-416, REGRESSION ANALYSIS
• Professor: All

Document Summary

The usual linear regression model assumes that all the random error components are identically and independently distributed with constant variance. When this assumption is violated, then ordinary least squares estimator of the regression coefficient loses its property of minimum variance in the class of linear and unbiased estimators. In such cases, the covariance matrix of random error components does not remain in the form of an identity matrix but can be considered as any positive definite matrix. Under such assumption, the olse does not remain efficient as in the case of an identity covariance matrix. The generalized or weighted least squares method is used in such situations to estimate the parameters of the model. In this method, the deviation between the observed and expected values of iy is multiplied by a weight i i is chosen to be inversely proportional to the variance of where. For a simple linear regression model, the weighted least squares function is iy .