Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.
3
votes
0answers
86 views
How to compare the similarity between functions?
I'm designing a web service that finds the regression function of a pattern within an image.
I analyzed three images and found the following three regressions:
1) $f(x) = 74.7602 + 0.2005x - ...
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 ...
3
votes
0answers
100 views
How to perform nonlinear regression with correlated errors?
I have a nonlinear least squares problem, but the errors are correlated. I could use R's nls function to do the regression if the errors were independent, but I don't know the right way to handle ...
3
votes
0answers
145 views
Least Square Method with Positive Parameters
this is my first post here in the Stack Exchange. A friend told me about this forum and I'm giving it a try.
I searched a bit past threads, but couldn't find what I wanted, so I'm posting the problem ...
2
votes
0answers
56 views
Minimizing L4/ L6/ L2N norm for linear regression
OLS regression minimizes the sum of the squared errors. The normal equation for an OLS for $L_2$ minimization is as follows: $$b= (A'A)^{-1}A'y$$
What would be the equation to minimize the $L_4$ norm ...
2
votes
0answers
46 views
Orthonormal Matrix weighted regression
$Q$ is a rectangular matrix with orthonormal columns. A linear system composed of $$Qx= b$$ is really easy to solve as:
$$Q'Q=I$$
hence:
$$x=Q'b$$
Given that $Q$ is orthonormal can this be used to ...
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 $ ...
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
votes
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"
...
2
votes
0answers
70 views
Bare minimum of points in multiple polynomial regression
I have a question on multiple polynomial regression and the absolute minimum amount of points in the different terms. The minimum amount of points required for a second order polynomial would (in one ...
2
votes
0answers
77 views
Find $w$ as the minimizer of regularized logistic regression
Could someone point me to a reference on how to find $w$ as the minimizer of:
$$
\frac{1}{2}\sum_{i=1}^{d}q_i(w_i-m_i)^2+\sum_{j=1}^{n}log(1+\exp(-y_jw^Tx_j))
$$
where $q_i$ (initialized with ...
2
votes
0answers
122 views
Logistic regression algorithm in Casio and Texas Instruments calculators
When using logistic regression on a Casio or Texas Instruments calculator, the output is of the form
$$f(x) = \frac{c}{1+ae^{-bx}} $$
The problem I have (when teaching in a class where both types of ...
2
votes
0answers
188 views
Finding a model for multiple non-linear regression
I want to implement a regression analysis, but I have problems with finding a model for the given data. There are $149$ $(x,y,z)$-values. $y$ values are all positive, $x$ is between $[-10, 10]$ and ...
2
votes
0answers
524 views
Correlation and Regression Question
Two separate tests are designed to measure a students ability to solve problems. Several students are randomly selected to take both tests and the results are:
$$
\begin{matrix}
\text{Test A}(x) ...
2
votes
0answers
778 views
Help with problem: Estimated Standard Deviation of Regression Equation (Simple Linear)
This is a practice problem. I've solved part (a). I have provided verified answers (from the published key) to all parts (a), (b) and & (c). I need help solving (b) and (c).
Consider a simple ...
2
votes
0answers
159 views
Surface Function Fitting to Spherical Data
I have a set of geographic (longitude,latitude,value) data to which I would like to fit surface functions, specifically, the set of quadratic surfaces:
$f(x,y)=Ax^2+Bx^2+Cxy+Dx+Ey+F$
At the moment, ...
2
votes
0answers
57 views
Accurate computation for Linear Regression case
I am writing a program that inputs a sequence of points $(x_i,y_i)$ based on the user clicking on certain pixels in an image shown. The program should then find the "best -fitting" line in the least ...
1
vote
0answers
60 views
How to calculate probability with sigmoid output in feedforward neural network?
first of all I'm sorry for my not very skilled English, but I will do my best to explain my problem.
I'm trying to create a feedforward neural network with one hidden layer (with probably arctan ...
1
vote
0answers
20 views
regression coefficient
Consider observations on three variables X1;X2 and X3: Suppose that
X1 is regressed on X2: When the residual of the above regression is
regressed on X3; the regression coefficient of X3 is b3: When X1 ...
1
vote
0answers
25 views
About the weights assigned in the linear regression
I have this confusion related to linear regression. Lets say I have two predictors $x_1$ and $x_2$ and the target is $y$. I learn a linear regression with $y \sim x_1,x_1 \cdot x_2,x_2$ with $x_1 ...
1
vote
0answers
31 views
Sequential problem for n=1, non linear regression
I am trying to understand an example in my stats course notes, the example relates to calculating the best value for the next experiment.
The function of the line is very simple:
$$ln(Y_i) = ...
1
vote
0answers
39 views
Correlation coefficient.
A linear regression gives us a correlation coefficient $r=0$.
What is the equation of the best fit line?
Give an example of data with $r=0$
What is the value of the correlation coefficient of data ...
1
vote
0answers
20 views
Coefficient of determination
$$ \displaystyle \sum^n_{i = 1} (y_i - \bar{y})^2 = ( \displaystyle \sum^n_{i = 1} (y_i - \bar{y})^2 - \displaystyle \sum^n_{i = 1} (y_i - \hat{y}_i)^2 ) + \displaystyle \sum^n_{i = 1} (y_i - ...
1
vote
0answers
38 views
Show that $Y$ has constant regression with respect to $X$ and/but that $X$ and $Y$ are not independent.
The joint density of $X$ and $Y$ is given by
$$ f(x,y) = \left\{
\begin{array}{l l}
1/2 & \quad \text{$|x|+|y|\leq 1$}\\
0 & \quad \text{otherwise}
\end{array} \right.$$
Show ...
1
vote
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 ...
1
vote
0answers
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" ...
1
vote
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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
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: ...
1
vote
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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
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.
1
vote
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:
...
1
vote
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
...
1
vote
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 ...
1
vote
0answers
96 views
1
vote
0answers
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 ...
1
vote
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 ...
1
vote
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, ...
1
vote
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 ...
1
vote
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, ...
0
votes
0answers
16 views
Calculate the tendency of a set of samples
I develop an application in which I constantly get samples of heart pulse.
I defined an interval of $t$ seconds.
In each $t$ seconds I have $n$ samples.
In every interval, I want to calculate the ...
0
votes
0answers
16 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, ...
0
votes
0answers
18 views
0
votes
0answers
46 views
Generating an equation from an image I have
I am not exactly sure if this question belongs here but I could not think of a better place to ask.
So I recently discovered that various people on the internet have created equations for rather ...
0
votes
0answers
31 views
If $\underset{n \times n}{M}$ is a symmetric and idempotent matrix having rank $r$
If $\underset{n \times n}{M}$ is a symmetric and idempotent matrix having rank $r$ then
$$w'Mw \sim \sigma^2 \chi^2_{(r)}$$
where $\underset {n \times 1}{W} \sim N(0,\sigma^2 I)$
that is, $w_i \sim ...
0
votes
0answers
18 views
Simple calculation problem in linear regression model
Define
$$Y_i=\beta_0+\beta_1 X_i+\epsilon_i$$
$$\bar Y=\beta_0+\beta_1 \bar X+\bar \epsilon$$
$$\bar Y=\frac{\sum_{i=1}^{n} Y_i}{n}$$
$$\bar X=\frac{\sum_{i=1}^{n} X_i}{n}$$
$$\bar ...
0
votes
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 ...
