Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.
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23 views
Extrapolating parameters for a fit different from the one originally used for regression analysis (no longer having access to data)
Say I have some data, I assume a fit of the form: $\alpha_1 e^{\beta_1 k}$, and I extract some values $\alpha_1>0$ and $\beta_1<0$ for $k=[1,\ldots]$. Say this appears to be a "near perfect" ...
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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 ...
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0answers
36 views
Regression with multiple line types from set of points
Given a set of points, I'm looking to find the best possible line (within reason) to fit to these points. These points won't be from real data, so they could form any sort of curve or line. So, I ...
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0answers
28 views
Comparison of variances between multiple time-series
I am trying to perform a comparison of variances of multiple time-series (weekly average prices). I have found a multiple linear regression model for each respective series with a lag model. Is it ...
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0answers
48 views
Finding the best fitting square
I have to find the best fitting square using the total least squares method. First we we had to find the best fitting rectangle using the following equations:
s1: $c1+ax+by=0$, $a^2 +b^2 =1$
s2: ...
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0answers
56 views
Fitting curve for Newton's cooling law data programatically?
The data are for the model $T(t) = T_{s} - (T_{s}-T_{0})e^{-\alpha t}$,
where $T_0$ is the temperature measured at time 0, and $T_{s}$ is the temperature at time $t=\infty$, or the environment ...
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1answer
46 views
Distribute a number in an exponential way in a certain number of times
I have a number $X$ (let say it's 100). I want to 'split' it$N$ times in a 'exponential' looking way.
For instance $y = 0,2692x^{-0,925}$ with $x$ the integers between 1 and 16 is working fine.
The ...
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0answers
11 views
What is the meaning of errors of separate variables in a fit?
When doing a least-square fitting of a two-parameter function (e.g. $y=a+bx$) with specialised software like Origin or gnuplot, one gets errors for the resulting $a$ and $b$. What do these errors mean ...
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1answer
79 views
Convergence in distribution and OLS in the regression model
Suppose a random variable $X_n$ converges in distribution to X and $E[X]< \infty$,
Is this statement true or is there any condition to satisfy this?
$ plim_{n\to \infty}Var(X_n) = Var(X) $ ...
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0answers
18 views
T-Value And Significance (SLR in R)
I am currently trying to figure out the output I got from the summary-command when I do a linear regression in R.
I get 2 values that I do not understand, first: the t-value. I do understand that it ...
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1answer
183 views
Binary Logistic Regression Model Processing
Thanks for showing interest and wanting to help out.
My aim is to develop a model that - as accurately as possible - predicts how entities in a population will either cooperate or defect, as a % of ...
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1answer
36 views
Interpret overall fitness in prediction
I came through this equation and would like to learn more about how to inteprete it.
d is defined as actual value, and $\hat{d}$ is defined as predicted value.
Why does this equation
(a) divides sum ...
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2answers
73 views
Multiple regression with model $Y = (1 + c_1X_1)(1 + c_2X_2)\ldots(1 + c_nX_n)$
I'm currently working with data contained in $Y, X_1, X_2, \ldots, X_n$ and wish to fit it to the model:
$Y = (1 + c_1X_1)(1 + c_2X_2)\ldots(1 + c_nX_n)$
where the $c_i$ are coefficients to be ...
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1answer
80 views
Quadratic function as a linear function
I am taking a machine learning course and today we were given an example of regression, with two attributes $x_,x_2$ and $y$ being the real valued outcome.
$y$ is a quadratic function of $x_1,x_2$, ...
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0answers
114 views
Fitting a 3d point cloud with a polynomial surface
I have 3D point cloud and I would like to fit a polynomial surface to it.
Could anybody please explain the step by step process to that.
Thanks a lot.
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0answers
1k views
Derivation of standard error of beta in simple linear regression
Countless web pages show the equation for the standard error of the slope in a simple linear regression. For example:
...
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2answers
70 views
Calculating the MLE for mu(x) in a regression model
Say we have the following regression model:
$$Y_i = \alpha + \beta(x_i - \mathrm{mean}(x)) + R_i$$
where $R_1,\ldots,R_{20} \sim G(0, \sigma)$
If we have $\mu(x) = \alpha + \beta(x - ...
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0answers
156 views
Confusion regarding confidence interval
I was using matlab's cftool to fit a regression line to my data point x and y. And I could see this
...
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0answers
84 views
Jacobian approximation at given point without explicit derivatives expression
after solving a NLproblem with optimization method, I would like to compute confidence intervals, prediction bounds and standard deviation for these optimal parameters. Explicit formulas I have read ...
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0answers
96 views
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46 views
Books on Function approximation and Regression
Can you suggest books/articles on Function approximation
Let me quote from the above wiki:
Second, the target function, call it g, may be unknown; instead of
an explicit formula, only a set of ...
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0answers
287 views
Moore–Penrose pseudoinverse reference
Given the eigendecompositions $AA^{\top}=Q \Lambda Q^{\top}$ and $A^{\top}A=P \Lambda P^{\top}$, where $\Lambda$ is a diagonal matrix (of eigenvalues) and $P$ and $Q$ are unitary eigenvectors matrices ...
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0answers
173 views
Point-wise error estimate in polynomial regression
In our application we wish to estimate the actual path of objects. We have a set of samples of object locations $(t_i, x_i, y_i, P_i)$ where $t_i$ is the sample time, $(x_i, y_i)$ is the 2D location, ...
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1answer
48 views
Is there a name for this general problem (variation on least squares)?
The problem statement is as follows.
Minimize $||g(X\beta)-y||^2$ with respect to $\beta$ where $g(\cdot)$ is some non-linear function, $y$ and $\beta$ are column vectors.
General linear least ...
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0answers
43 views
Need practical help with a calculation
I'm sorry for a really basic question. I lack proper background in mathematics, but I have to calculate a list of values.
I'm given a vector (list) of observations, and $\hat{Y}$, which is a list of ...
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0answers
37 views
Finding a confidence interval for a parameter of regression given two variable variances
Given an equation $Y_i=0.1+0.3x_i+e_i$, I am asked to calculate a 95% confidence interval for $Y_i$ when $x=0$. So I have an equation $Y_i=0.1+e_i$, and I know that standard error of 0.1 is 0.005, ...
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1answer
186 views
Real World Examples of Sinusoidal and Logistic Functions (and Regression)?
Anyone ever use a real world example (or data) of either:
1) Sinusoidal Regression
2) Logistic/Log Regression
This can alternatively be answered by identifying any real world functions that ...
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2answers
23 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 ...
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1answer
76 views
Function description
I have function looks like this:
So, the point is after it comes to steady state, it slowly goes down. How can I describe such a behaviour?
The datapoints are:
...
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votes
1answer
844 views
Multiple vs Single Linear Regression
I'm having trouble understanding the relationship between multiple and single linear regression. I have six variables $(x_1, \dots, x_6)$ I'm using in my model. If I check each one individually ...
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1answer
72 views
Getting linear regression of huge numbers
I'm trying to get a linear regression slope and intercept for a large set of huge numbers.
I'm doing this on a computer, but I keep getting overflow errors (attempting to calculate a number too large ...
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2answers
157 views
General nonlinear least squares?
I'm looking to solve some kind of generalized nonlinear least squares problem, I think.
So for some background, lets say I have an ordinary nonlinear least squares problem. That is, a set of data ...
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2answers
60 views
Greater precision with regression?
I used my TI-83 to find the quadratic regression of two data columns. The accuracy wasn't close at all. So I tried cubic and then finally quartic regression. The accuracy still isn't close enough. Is ...
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2answers
404 views
regression (using 3D points cloud dataset)
I have a dataset of trajectories. These trajectories are represented in 3D space (x,y,z). All trajectories of this dataset are similar in their shape, but they are not exactly the same, I mean, there ...
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1answer
52 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:
$y = c + \sum_{i=1}^n k_i x_i + \varepsilon_i$,
...
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1answer
59 views
Non-Linear regression
Imagine that I have a function $ f(x,y) $ to model a physical phenomenon.
I believe that functions is defined by $$ f(x,y) = A*x + B*y + C*x*y$$
I have many values for $ (x,y,f(x,y)) $, how can I ...
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2answers
259 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 ...
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1answer
120 views
Intersection line of planes
There are 2 planes:
$Q: 2x-y=2$
$R: x-y-z=1$
How do I find the line $p=(1,2,-1)$, which intersects $Q$ and $R$ plane.
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votes
1answer
65 views
Fit predetermined curve to data set
I have a set of $5$ data points $(x, y)$. I need to find two constants ($a$ and $b$), so that the curve $x\cdot y^a=b$ fits my data set. The question states that I can find the constants from the ...
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1answer
138 views
Regression question - Weak exogeneity
The typical assumption of linear regression, weak exogeneity, states, $$E(\bf{\epsilon_{i}})=0$$ when the regressors are fixed and $$E(\bf{\epsilon_{i}}|\bf{x_{i}})=0$$
when the regressors are random.
...
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votes
2answers
192 views
Least Squares Fitting - Logarithmic
Is there any software that will fit a set of 2D points using a logarithmic curve?
I found this, which looks like the formulas I need, but I don't think I have a fancy enough calculator to solve that ...
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votes
2answers
121 views
“Proof” of an Algebraic property of OLS Estimators
I'm having a bit of trouble proving $\sum (x_i - \bar{x})\hat{e_i} = 0$. What I know so far is that the total sum of $\hat{e_i}$'s is zero by property of OLS so when you distribute the $\hat{e_i}$ ...
0
votes
2answers
180 views
linear regression analysis
i am given data for analysis following data:relationship between height and weight,question is :is relationship between them linear?like
$y$=$a$+$b$*$x$+$e$
where e is error,or quadratic?or ...
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1answer
159 views
dependency between regression coefficients and probability distribution
let's consider regression problem. Given set of training data $\{(x_i,y_i)\}_{i=1}^N$, $x_i \in \mathbb{R}^n$ and $y_i \in \mathbb{R}$, find prediction function $y = f(x)$, e.g. in RBF regression case ...
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votes
1answer
70 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 ...
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1answer
62 views
Forecasting using multiple regression
I have data in the form given below, and I want to perform forecasting using multiple regression. I found definition of multiple regression from this link: http://otexts.com/fpp/5/1/ . I have these ...
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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 ...
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1answer
225 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 ...
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1answer
64 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 ...
