All Questions
16
questions
5
votes
1
answer
45
views
In Regression Through the Origin, why do the CIs of the slope depend on datapoints with zero x value?
I'm working with a Regression Through the Origin model as described in this reference.
The model is $Y_i = \beta X_i + \epsilon$ and the least squares estimate of $\beta$ is $\hat\beta = \frac{\sum ...
- 151
2
votes
1
answer
2k
views
What is the impact of duplicate data on the variance of regression coefficient? [duplicate]
What is the impact of duplicate data on the variance of the regression coefficient?.
Does increasing the size of data always certainly decrease the variance of the model coefficients?
Suppose I have ...
- 223
0
votes
1
answer
80
views
Calculating variance / standard errors for a Weighted Repeat Sales model
I'm writing an implementation of the Case-Shiller Real Estate Index, which is based on a variation of the weighted least squares, except for the introduction of a dummy matrix Z. I've calculated the ...
- 101
0
votes
0
answers
28
views
Where does (co)variance come from in a linear (OLS) regression?
Given that linear models can be solved exactly via calculus, how is it possible to define a variance for the parameters ($\mathbf{a}$) which minimize some error function? say $Err=(o_i-f(x_i; \mathbf{...
- 143
0
votes
0
answers
166
views
Question about confidence intervals and prediction intervals
Considering following linear multiple regression model:
\begin{equation}
y=X\beta + e,
\end{equation}
where observations $y\in\Re^n$, coefficents $\beta\in\Re^p$ and $e\sim N(0,\sigma I)$ is a white ...
- 235
4
votes
1
answer
4k
views
Calculating confidence intervals for the variance of the residuals in R
I have three variables:
Number of house sales
Month (in couples)
Region of a city (N-W-E-S)
and I want to calculate confidence intervals for the residual of the errors. So, given the data:
...
- 173
4
votes
2
answers
292
views
Linear model – confidence interval for $\sigma$
I'd like to derive a $100\%(1-\alpha)$ confindence interval for $\sigma$ in a linear model $Y=X\beta+\epsilon$, $X$ - $n\times p$. I thought that I could make use of the fact that:
$\frac{RSS}{\sigma}=...
- 390
1
vote
0
answers
25
views
How to estimate the confidence interval for a "predicted difference" from a quadratic model?
Assume you have past consumption levels $c_1, \dots c_n$ at times $t_1, \dots t_n$ and cumulated consumption levels $y_1=c_1, y_2 = c_1 + c_2, \dots y_n=\sum_{k=1}^{n} c_k$.
(I use the quadratic term ...
- 209
0
votes
0
answers
1k
views
Pointwise standard error and confidence interval for a smoothing spline
I wish to generate confidence intervals for a smoothing spline using the pointwise standard error of $\hat{f}_\lambda(x)$. In particular, I am trying to construct the following interval: $$\hat{f}_\...
- 556
1
vote
0
answers
36
views
What do we use variance of the error term for in regression analysis?
So I get that, for simple linear regression where Y = B_0 + B_1(x) + E, Var(Y|x) = Var(E). Variance of the mean response involves it, as does variance of future responses, but is this ever actually ...
- 11
2
votes
2
answers
99
views
How to calculate the confidence interval of a line based on its coefficients?
I fitted a mixed model as following:
$Y = \beta_0 + \beta_1 T + \beta_2 X + \beta_3 X T + \beta_iW_i$
$T$ is time, $X$ is my variable of interest and $W_i$ are various confounding variables. I also ...
- 1,440
1
vote
1
answer
1k
views
Why do we include the variance of $\epsilon$ for the variance of predicted values? (normal linear models)
Suppose I have a normal linear model $Y = X\boldsymbol{\beta}+\epsilon$, $\epsilon \sim N(0,\sigma^{2}I_{n})$. Given covariates $x_{*}$ and estimated parameter vector $\hat{\boldsymbol{\beta}}$, I ...
- 649
1
vote
1
answer
355
views
Confidence Interval derivation
I am predicting a "yearly cumulative variable" from monthly results.
I use $Y_j = \sum_{i=1}^j (X_i) / f_i$ where $j$ is the current month.
I know the $f$ from history; e.g. January = .073, ...
- 11
4
votes
1
answer
1k
views
Confidence interval for variance in simple regression model
I am attempting to create a confidence interval for $\sigma^2$ in simple regression model $$ Y_i = \beta_0 + \beta_1 x_i + \epsilon_i , \ \ \epsilon_i \sim \text{ Normal(0, $\sigma^2$)} $$
We know ...
- 41
8
votes
1
answer
932
views
Are group effects in a mixed effects model assumed to have been picked from a normal distribution?
Say we're interested in how student exam grades are affected by the number of hours that those students study. We sample students from several different schools. We run the following mixed effects ...
- 14.5k