# Linked Questions

21 questions linked to/from Why is RSS distributed chi square times n-p?
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### Linear regression: Unbiased estimator of the variance of outputs [duplicate]

I'm having trouble understanding something from the linear regression chapter of Elements of Statistical Learning. We have a fixed $N\times p$ matrix $\mathbf{X}$ ($N$ inputs with $p$ predictors) ...
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### Residual Sum of Squares degrees of freedom intuition [duplicate]

Let RSS = Residual sum of squares $= \sum (y_i - \hat{y}_i)^2$. Without proof, $\frac{RSS}{\sigma^2} \sim \chi^2_{n-2}$. I do not quite understand why the DoF is $n-2.$ Could someone explain?
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### Why is a T distribution used for hypothesis testing a linear regression coefficient?

In practice, using a standard T-test to check the significance of a linear regression coefficient is common practice. The mechanics of the calculation make sense to me. Why is it that the T-...
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### What is “estimated unbiased variance of the error term”?

Disclosure: This is a homework question. I have fit a multiple linear regression model in eviews, and I am asked to calculate "estimated unbiased variance of the error term, i.e., $\hat\sigma^2$". ...
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### Proof that regression residual error is an unbiased estimate of error variance

Consider the least squares problem $Y=X\beta +\epsilon$ while $\epsilon$ is zero mean Gaussian with $E(\epsilon) = 0$ and variance $\sigma^2$. I need to prove that $\frac{V(\hat{\beta})}{N-(n+m)}$ ...
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### Why use the F distribution and F test?

I don't understand why in the F test we calculate the ratio between MSE between subject and MSE within subject. As far as I know, this is due because we want to use the F distribution, which is a rate ...
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### Why is the MLE for variance in single linear regression biased? [duplicate]

I understand that the Maximum Likelihood Estimator for variance, in general, is biased (the average calculated from the sample itself reduces the degree of freedom by 1 e.t.c): ...

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