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Finding the distribution in OLS

The distribution will be $t_{n-2}$. Below, I assume the sample $\{x_i\}_{i=1}^n$ is treated as fixed. That is, I do all computations as if we were conditioning on $\{x_i\}_{i=1}^n$. I relax this ...
Joseph Basford's user avatar
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In a regression of Yon X, the value of X is fixed at 5. Find the regression equation

If there is no constant in the regression, then $$ \widehat{\beta} = \frac{\sum_i x_iy_i}{\sum_i x_i^2} = 5\frac{\sum_i y_i}{5^2N} = \frac{\bar{y}}{5}.$$ It is not a slope, however, as $x_i$ is ...
Bertrand's user avatar
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In a regression of Yon X, the value of X is fixed at 5. Find the regression equation

If $X$ is constant it is impossible to find the regression equation because regression coefficients $\beta_i$ are given by: $$\beta_i = \frac{cov(Y, X_i)}{var(X_i)}$$ if you fix $X$ to be always 5 the ...
1muflon1's user avatar
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