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List of top Estimation Questions on Ordinary Least Squares Estimators asked in GATE ST

Let \( Y_i = \alpha + \beta x_i + \epsilon_i \), where \( x_i \)'s are fixed covariates, \( \alpha \) and \( \beta \) are unknown parameters, and \( \epsilon_i \)'s are independent and identically distributed random variables with mean zero and finite variance. Let \( \hat{\alpha} \) and \( \hat{\beta} \) be the ordinary least squares estimators of \( \alpha \) and \( \beta \), respectively. Given the following observations: 

The value of \( \hat{\alpha} + \hat{\beta} \) equals _________ (round off to 2 decimal places).

  • GATE ST - 2021
  • GATE ST
  • Estimation
  • Ordinary Least Squares Estimators