How are $\hat{\beta}$ and $\hat{\sigma}^2$ independent in OLS when assuming that $\epsilon \sim N(0, \sigma^2)$?
45114
Why is a T distribution used for hypothesis testing a linear regression coefficient?
20900
Regression without intercept: deriving $\hat{\beta}_1$ in least squares (no matrices)
134510
How do you get $\rm{var}(\Theta -\hat\theta) = \rm{var}(\Theta)$?
137826
How is MSE divided by $\sigma^2$ always a chi-square distribution?
28006
The minimum of two independent geometric random variables
18967
Linear independence of $\sin(x)$ and $\cos(x)$
76853
Interpretation of $\mathbf{y}^T(\mathbf{I}-\mathbf{H})\mathbf{y}$ in OLS
131026
Covariance and independence?
20153
What is the distribution of $R^2$ in linear regression under the null hypothesis? Why is its mode not at zero when $k>3$?
118867
Independence of Gaussian variables
127052
Independence of non-constant real variables
91087
For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
84203
Let $X_1$ and $X_2$ are independent $N(0, \sigma^2)$ random variables. What is the distribution of $X_1^2 + X_2^2$?
39548
Multicollinearity in OLS
67489
How to show that $E[(\hat\theta -\theta)^2]<Var(\bar X)=\dfrac{1}{n}$?
7970
Why does the product of the bivariate regression coefficients of the $y$-on-$x$ line and $x$-on-$y$ line equal the square of the correlation?
26961
How do I calculate standard errors for sums of OLS coefficients?