Tagged Questions
1
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1answer
22 views
Simple Linear Regression Question
Let $Y_{i} = \beta_{0} + \beta_{1}X_{i} + \epsilon_{i}$ be a simple linear regression model with independent errors and iid normal distribution. If $X_{i}$ are fixed what is the distribution of ...
0
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0answers
13 views
Multivariate regression
What is the most suitable way to assess the effect several independent ordinal variables have on a single nominal variable ?
For example the chance of a tumour being malignant predicted by the
1. ...
2
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2answers
34 views
Linear Regression: Expectation Proof
I found the following proof in my notes:
$E(Y_i) = E[\beta_0 + \beta X_i + \varepsilon_i] =\cdots= \beta_0 + \beta X_i$. This does not seem right to me, however. Why would $E(\beta_1 X_i) = \beta_1 ...
0
votes
2answers
25 views
Is a Relationship Quadratic?
I have a relationship $y=f(x)$ for which I can obtain data through simulation.
I have good reason to suspect that this relationship is quadratic (rather than, say, exponential), and would like to ...
0
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0answers
18 views
Stata: “Between and fixed effect estimates” in a linear regression?
I'm working on a paper by B. H. Baltagi and I am trying to replicate the results. It can be found here, the data is here. I'm supposed to do a linear regression - sounds simple. The author uses Stata, ...
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0answers
18 views
0
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1answer
73 views
Prediction Model for forecasting using Linear regression
I am very new to inferral statistics. I am trying to build a prediction model for forecasting the revenue for physicians based on some historical data. I was planning to use Multiple Linear Regression ...
1
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0answers
31 views
Sequential problem for n=1, non linear regression
I am trying to understand an example in my stats course notes, the example relates to calculating the best value for the next experiment.
The function of the line is very simple:
$$ln(Y_i) = ...
0
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0answers
41 views
What is the difference between random and nonrandom?
In a simple regression model $Y_i=\beta_0+\beta_1 X_i+\epsilon_i$, $X_i$ is nonrandom.
But we don't know $\beta_0, \beta_1$ value (we should estimate them in our model), $Y_i$ is random.
I wonder what ...
1
vote
1answer
111 views
How to find a line of best fit of the form $y=ax$?
We have the following points:
$$ (0,0)(1,51.8)(1.9,101.3)(2.8,148.4)(3.7,201.5)(4.7,251.1)(5.6,302.3)(6.6,350.9)(7.5,397.1)(8.5,452.5)(9.3,496.3)$$
How can we find the best fitting line $y=ax$ ...
1
vote
1answer
44 views
What is the way to determin how good a sequence will interpolate?
Say I have to sequences of numbers:
$$[5, 10, 14, 21, 27, 31]$$
$$[1, 20, 21, 22, 30, 31]$$
Even though they both get to $31$ by the $6$th element, logic tells me that only the first one is a good ...
2
votes
1answer
38 views
Why is $\sum x^2 _t \times \text{Var}(\beta)=\frac{\sum x^2 _t \times \sigma^2}{ \sum x^2 _t} = \sigma^2$?
I do not get this connection.
Is is reliable to divide this equation by $\sum x^2 _t$ to get just $\sigma^2$ ?
$$\sum x^2 _t \times E(\hat \beta - \beta)^2=\sum x^2 _t \times ...
0
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0answers
24 views
Is $x_3$ important in the second model?
A data set contains $n= 32$ observations on four variables $y,x_1,x_2$ and $x_3$. Model $y=\beta_0 + \beta_1 x_1 +\beta_2 x_2 + \epsilon$
produced $R^2 = 0.8806$. But model $y = \beta_0 + \beta_1 x_1+ ...
0
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1answer
53 views
How to solve multi-variate linear regression analytically?
We have $n$ variables $x_n$ and one stochastic function $y$ of these variables. We assume that function $y$ depends on variables in the following way:
$y = c + \sum_{i=1}^n k_i x_i + \varepsilon_i$,
...
0
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0answers
25 views
Calculate the estimated residual series $\hat{u}_t = y_t + b_{OLS}$
I am struggeling with this excercise:
Use this data and the simple model $y_t = β + u_t$ and calculate the estimated residual series
$$\hat{u}_t = y_t + b_{OLS}$$
using the least squares estimator ...
1
vote
1answer
32 views
Cointegration for Price levels Time Series
I don't understand why is the difference between price levels is a stationary process while the time series of price levels themselves is a non-stationary process.
For example:
...
0
votes
1answer
38 views
Regression Proof
If the joint density function of $X$ and $Y$ is given by: $$f(x,y)= \begin{cases}
1/2, & \text{for } |x| + |y| \le 1 \\ 0, & \text{otherwise} \\ \end{cases}$$
Show that $Y$ has constant ...
0
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0answers
19 views
What's the difference between fixed design and random design?
I am thinking about the regression problem of random design.
Consider the model $Y=X\beta+\varepsilon$, where $X\in \mathbb{R}^{n*p}$.
I know that under the fixed design, if we have that the $i$-th ...
0
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0answers
34 views
Finding a closed-form formula for the variance of the absorption direct estimator
I need to solve a system of linear equations via monte carlo methods, i.e.
$$Ax=B$$
I need to derive the a formula for the variance of an estimator given that the estimator is equal to:
- let $Q$ be ...
0
votes
1answer
32 views
Minimizing a function with vectors
This is a part of a problem that I'm having, and I'm unclear how to do this particular step. I'm dealing with a ridged regression and I need to minimize the equation
$$\sum (Y_i - \beta^Tx_i)^2 + ...
0
votes
1answer
232 views
Matlab Time Series (AR, MA, ARIMA)
Is there a function which calculates an AR(p), MA(q), ARIMA(p,q) process in MATLAB which is free. I know of Econometrics toolbox, but I have to pay for that. Is there a way to get around that?
0
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1answer
42 views
What is a “recurrent model” in forecasting
In this book, there is a chapter titled Recurrent Models (you can see that chapter in Google books) but it's very short and some parts are not very clear to me. Recurrent Models seem to refer to a ...
1
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0answers
53 views
Formula for confidence interval in multi-variable regression
What is the formula for calculating the confidence interval for the expected value of $\hat{y}$ in a multi-variable regression model.
In other words, I'm looking for the following formula just for ...
2
votes
4answers
271 views
Given a data set, how do you do a sinusoidal regression on paper? What are the equations, algorithms?
Most regressions are easy. Trivial once you know how to do it. Most of them involve substitutions which transform the data into a linear regression. But I have yet to figure out how to do a ...
0
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0answers
31 views
Standard deviation of a particular dimension in a multivariate Gaussian distribution
I have a set (cluster) of vectors in dimension $d$. From this I have calculated the sample mean and covariance matrix ( I make the assumption that they are from a multivariate Gaussian).
My question ...
0
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0answers
26 views
Regression Model Estimator
Assume regression model $y_i = \alpha + \beta x_i + \epsilon_i$ with $E[\epsilon_i] = 0, E[\epsilon^2] = \sigma^2, E[\epsilon_i \epsilon_j] = 0$ where $i \ne j$. Suppose that we are given data in ...
0
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0answers
27 views
What to do when the predictors do not accord with common sense/literature, but the model is fine/best according to log likelihood and LRT?
down vote
favorite
I would try to clarify the problem and then ask the questions.
The problem (variable names are masked due to confidentiality):
I ran a binary logistic regression, in which there ...
0
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1answer
68 views
Does Principal Component Regression still work in high-dimensional ($N<p$) situation?
I understand that, many classical methods for multiple regression won't work when $N<p$, where $p$ is the dimension of the input space and $N$ is the sample size.
For example, LSE for multiple ...
2
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1answer
81 views
What am I reinventing? RE: Linear regression modeling for frequency of discrete events
I'm looking to model the frequency of events to quantify how much that frequency is increasing or decreasing. For the sake of concreteness think of the events as web page hits for several low traffic ...
0
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1answer
47 views
Linear Models - Regression Analysis
As a student learning Applied Regression Analysis, I come from a background with very little information about this topic.
I understand that given $y = \beta_0 + \beta_1x_1 + \epsilon$
$E(y|x) = ...
1
vote
1answer
125 views
What is the difference between a polynomial regression and a generalized linear model?
I have seen that a polynomial linear regression can have this form:
$y = c_0 + c_1 x_1 + c_2 x_2 + \dots + c_k x_k $
but I have read that the general lineal model which is a form of the multiple ...
-1
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1answer
112 views
When to use likelihood ratio test? [closed]
I have a few questions regarding the use of likelihood ratio test in a logistic regression model.
Suppose we have a logistic regression model like this:
...
0
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0answers
78 views
Regression with Binary Variables in R: Should have 4 regression lines, only getting 1.
I'm using R for this regression model. Since I have two binary variables in my model, I should end up with 4 regression lines, but I'm not seeing how to plot all of them at once. I already used ...
0
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0answers
44 views
Standardized slope in monotonic data series
I am interested in comparing the slopes of 2 linear regressions in a meaningful manner.
The independent variable (x) is monotonic: 500, 1000, 1500, 2000, 2500, 3000, etc.
The dependent variable (y) ...
2
votes
2answers
59 views
Closed form for coefficients in Multiple Regression model
I want to find $\hat{\beta}$ in ordinary least squares s.t. $\hat{Y} = \hat{\beta}_0 + \hat{\beta}_1 X_1 + \cdots + \hat{\beta}_n X_n $. I know the way to do this is through the normal equation using ...
2
votes
1answer
287 views
Equations For Quadratic Regression
Does anyone know the specific equations for the three parameters in a least-squares quadratic regression? I'm looking for something like $\beta_1=,\beta_2=,\beta_3=$ for each of ...
3
votes
3answers
138 views
Does the Least Squares Regression Method work for any line type?
I recently learned how to apply the least squares method to do linear regression. I also understand that it can be used for quadratic regression, by minimizing the error for three variables, two ...
2
votes
0answers
46 views
Regressing $Y$ back on the residuals
Suppose I have the linear regression model $ \hat{y_i} = a + b x_i $ for $a,b$ obtained via OLS. How does one regress $y$ back on the residuals $\hat{e}_i = y_i - \hat{y}_i$? If we write $ ...
1
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0answers
37 views
Gaussian prior from feature to input space
if I have Gaussian prior ($\exp\left(\dfrac{-\sum_i w_i}{2\gamma^2}\right)$) on my weights in a linear classifier, how can I transform this so I can apply it for my kernel parameters $\alpha$? I have ...
0
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0answers
31 views
first set of timeseries data to predict second set
I have timeseries data with n=100 and have done a simple linear regression on the first 50 data points. What I'm interested in doing is seeing how good my y-hat line is at predicting the second 50 ...
0
votes
2answers
263 views
Normal Distribution from Standard Deviation?
So I have a data set $(x_{1},y_{1}), (x_{2},y_{2}),\dots,(x_{n},y_{n})$ and from it I have the values of $\sum x$, $\sum x^{2}$, $\sum y$, $\sum y^{2}$, $\sum xy$.
My question is, how do I find a ...
2
votes
0answers
54 views
Confidence Interval
I'm trying to find the best estimates for a and b by fitting the equation below to the data given $(y_{t}, C_{t})$
$$y_t=a*(1-e^{-b} ) / e^{bt} * \sum_{i=-20}^t {C_{x}e^{bx}+\gamma+\epsilon_t}$$
...
2
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0answers
48 views
Effective model for calculating momentum or growth rate for a time series
I have a series of numbers tracking the performance of an entity on any given day. It's nothing but a simple integer for each date. For example, here's a series for Entity "X"
...
0
votes
0answers
36 views
Linear-Regression Result Accuracy as a Function of Slope, Other Factors
Say I have the following functions
$ f(x) = Asin(Bx) $
$ g(x) = M_1x $
$ h(x) = M_2x $; where $M_2 \approx 0$ and $M_1 > 1000 M_2$
$ z(x) = C $
$ e(x) = N(0,\sigma) $
$ m_g(x) = f(x) + z(x) - ...
2
votes
1answer
61 views
Linear relationship of a company's profit
Assume a linear relationship for a company that has several shops is not known. Let $Y_i$ be the profit
the shop number $i$ makes in the coming year. Let $x_i$ be the size of
the shop number ...
3
votes
0answers
26 views
Regression model for a shearing process
30 Widgets are randomly assigned to a shearing process.
There are 3 such processes, each getting 10 widgets.
The lengths of each widget are recorded before undergoing the shearing.
The amount that ...
1
vote
1answer
210 views
Hat Matrix Identities in Regression
I need to show that $\bar h= \sum{h_{ii}/n} = \operatorname{Tr}[H]/n = (p+1)/n$
Using the fact that $\operatorname{Tr}[AB]=\operatorname{Tr}[BA]$ and $H=X(X^TX)^{-1}X^T$.
But I have no idea how to ...
0
votes
0answers
36 views
Confusion over a likelihood function involving a covariance matrix
I am working through a paper on global optimization using kriging. I can't tell if a term in one of the equations describes the determinant of a matrix, or what. We have $n$ observtions $y=(y_{1} ...
0
votes
0answers
75 views
Bootstrap sampling
The usual way to create bootstraps is by sampling with replacement from the original data set.
The resulting resampled bootstraps have the same length (N records/data points) as the original data ...
0
votes
1answer
119 views
Multiple Linear Regression - Multivariate Normal and Beta(ols)
I think this is probably supposed to be super easy - both questions are worth a total of one mark I've just never seen most of this before.
y=XB+E where B is beta and E is the error term.
E~MVN(0, ...
