The OLS estimator is a linear estimator, $\hat { \beta }$ ₁ = $\sum _ { i = 1 } ^ { n } \hat { a } _ { i } Y _ { i }$ , where $\hat a$ _i = A) $\frac { X _ { i } - \bar { X } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right) ^ { 2 } }$ B) $\frac { 1 } { n }$ C) $\frac { X _ { i } - \bar { X } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right) }$ D) $\frac { X _ { i } } { \sum _ { j = 1 } ^ { n } \left( X _ { j } - \bar { X } \right) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The correct formula for $\hat{a}_i$ in the context of the OLS estimator involves the numerator being the deviation of $X_i$ from its mean $\bar{X}$, and the denominator being the sum of squared deviations of all $X_j$ from their mean. This is accurately represented in option A.

The OLS Estimator Is a Linear Estimator β^\hat { \beta }β^​

The OLS Estimator Is a Linear Estimator $\hat { \beta }$