All Questions
Tagged with sum regression
11
questions
2
votes
0
answers
90
views
Decomposing the prediction of a sum of Gaussian Processes into predictions from each Gaussian Process
Suppose the functions $f_1\sim\mathcal{GP}(m_1,K_1)$ and $f_2\sim\mathcal{GP}(m_2,K_2)$ are drawn from independent Gaussian Processes, and let
$$f=f_1+f_2.$$
Then
$$f\sim\mathcal{GP}(m,K)$$
where $m=...
- 245
7
votes
3
answers
2k
views
If X=Y+Z, Is it ever useful to regress X on Y?
If we have X and Y that are mathematically dependent: X = Y + Z, is it 'forbidden' to use Y as a predictor to X in linear regression? I'm trying to find a concise explanation for why it is, or isn't.
...
- 85
1
vote
1
answer
60
views
Is the sum of 3 bits a linearly separable task?
In other words can a linear classifier learn to correctly assign a class (label 0 to 3) for an input of 3 bits? Intuitively this cannot work, since the half-adder circuit contains an XOR block, which ...
- 111
3
votes
1
answer
57
views
Is there a way to prove $\mathbf{\hat{Y}}^T\mathbf{e}=\mathbf{0}$ without resorting to summations?
I would like to show that $\mathbf{\hat{Y}}^T\mathbf{e}=\mathbf{0}$. I can solve this by saying that it is equivalent to showing $\sum e_i\hat{y}_i=0$. However, I'm wondering if there is a way to ...
- 2,103
1
vote
1
answer
75
views
residuals in the simple regression model
The residuals in the simple regression model have to sum up to 0?
1
vote
1
answer
5k
views
Linear regression $y_i=\beta_0 + \beta_1x_i + \epsilon_i$ covariance between $\bar{y}$ and $\hat{\beta}_1$
I am currently reading through slides from Georgia Tech on linear regression and came across a section that has confused me. It states for
$$
y_i=\beta_0+\beta_1x_i+\epsilon_i
$$
where $\epsilon_i \...
- 367
1
vote
1
answer
70
views
Value of $\sum_{j=1} (y_{j} - \bar{y})$ and proving properties of hat value
The i-th fitted value $\hat{Z}_i$ is written as a linear amalgam of response values $\hat{Z}_i=\sum_{j=1}h_{ij}Z_j$ where $h_{ij}=\frac{1}{n}+\frac{(y_i-\bar{y})(y_j-\bar{y})}{S_{yy}}$ and $S_{yy}=\...
- 367
2
votes
1
answer
3k
views
Notation for leads and lags in difference-in-differences
I was hoping someone could help clarify a notational discrepancy.
For example, Lord Pischke uses the following sigma notation in two different lecture notes published on the web, yet refers to the ...
- 6,244
0
votes
1
answer
133
views
Proving an identity involving $E(e_i^2)$ in simple OLS
Once expressed the simple OLS residual $e_i$ as a weighted sum of the noise terms:
\begin{equation}e_{i}=\sum_{j}\left(\delta_{i j}-\frac{1}{n}-\left(x_{i}-\overline{x}\right) \frac{x_{j}-\overline{x}...
- 76
6
votes
2
answers
596
views
Sum of predicted values to the power of 10 [closed]
When I take predicted values from a linear model to the power of 10, their sum is always a lot bigger than the original. Is it even allowed to sum, and does anybody have a reference for how this ...
0
votes
1
answer
8k
views
Regression proof for decomposition of sums of squares [duplicate]
I got as far as distributing the summation across the Left Side so that I have:
$$ \sum_i y_i^2 - \sum_i 2 y_i \bar{y} + \sum_i \bar{y}^2 $$
Not sure where to go from there.
- 1