Variance of Estimator: Learn How to Calculate

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SUMMARY

The discussion centers on calculating the variance of an estimator, specifically in the context of the linear model Y_i=βX_i+ε_i, where the estimator β is defined as \bar{Y} / \bar{X}. The user initially calculated the mean of the estimator as n*β and sought clarification on the variance calculation. The conversation highlights the importance of defining terms and understanding the underlying statistical concepts for accurate computation.

PREREQUISITES
  • Understanding of linear regression models
  • Familiarity with statistical estimators and their properties
  • Knowledge of variance and its calculation
  • Basic proficiency in mathematical notation and symbols
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  • Study the properties of estimators in linear regression
  • Learn how to calculate the variance of estimators in statistical models
  • Explore the concept of bias and consistency in estimators
  • Review examples of variance calculations in practical applications
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Statisticians, data analysts, and students studying regression analysis who seek to deepen their understanding of estimator properties and variance calculations.

trenekas
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Hi there. I would like to ask you one question about variance of estimator.

Suppose that Y_i=βX_i+ε_i and β estimator is \bar{Y} / \bar{X}.

I calculated mean of estimator. I am not sure if it's correct, but i got that its equal to n*β. But how about variance.
Any help would be appreciated!
 
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It would help if you could back up one step and define your terms.
 
I found a solution :) Thank you.
 

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