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Regression that includes two or more non-constant independent variables.

2
votes
1answer
If $\textbf{X}\in\textbf{R}^{n\times p}$ has full rank and $\textbf{Y}\in\textbf{R}^{n\times 1}$, prove that \begin{align*} \sum_{i=1}^{n}(Y_{i} - \hat{Y}_{i}) = 0 \end{align*} where $\hat{\textbf{Y} …
asked Mar 31 by user1337
0
votes
1answer
So here I am studying regression analysis. As an assignment, I have been asked to obtain some binary data, simulate its behavior from some sample of it and apply the resulting general linear model to …
asked Apr 6 by user1337
3
votes
1answer
Once again, here I am. Given the multiple linear regression model \begin{align*} \textbf{Y} = \textbf{X}\beta + \epsilon \end{align*} where $\epsilon\sim\mathcal{N}(\textbf{0},\sigma^{2}\textbf{I})$ …
asked May 16 by user1337
0
votes
1answer
I know this question is quite simple and maybe quite naive as well, but I would like to get some help. The general linear model can be expressed as \begin{align*} \textbf{Y} = \textbf{X}\beta + \epsil …
asked May 16 by user1337
1
vote
0answers
For $i = 1,2,\ldots, n$, consider \begin{align*} Y_{i} = \beta_{0} + \beta_{1}(x_{i1} - \overline{x}_{1}) + \beta_{2}(x_{i2} - \overline{x}_{2}) + \epsilon_{i} \end{align*} where $\overline{x}_{j} = \ …
asked Mar 31 by user1337
0
votes
1answer
Let $Y_{1},Y_{2},\ldots,Y_{n}$ be independent random variables with expected values $\mu_{1},\mu_{2},\ldots,\mu_{n}$, respectively. Suppose that the $\mu_{i}$'s are functions of the parameter vector t …
asked May 18 by user1337
0
votes
1answer
This is a follow-up question to 1 and 2. So we have the normal linear model \begin{align*} \textbf{Y} = \textbf{X}\beta + \epsilon \end{align*} where $\epsilon\sim\mathcal{N}(\textbf{0},\sigma^{2}\te …
asked May 17 by user1337