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MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 7: Dependent And Independent Variables, Linear Regression, Bias Of An Estimator

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rosi10agarwal
6 Apr 2023
School
Indian Institute of Technology - IIT Kanpur
Department
Mathematics
Course
MTH-416, REGRESSION ANALYSIS
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So the statistical inferences based on this will be faulty. 2s gives an overestimate of then also test and confidence region will be invalid in this case. If the response is to be predicted at x x x. 2 then using the full model, the predicted value is with y x b x x x. When the subset model is used then the predictor is y. 1 y is a biased predictor of y . X x the mse of predictor is. 444 n k : inclusion of irrelevant variables. Sometimes due to enthusiasm and to make the model more realistic, the analyst may include some explanatory variables that are not very relevant to the model. Such variables may contribute very little to the explanatory power of the model. This may tend to reduce the degrees of freedom ( and consequently, the validity of inference drawn may be questionable.

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