# Tagged Questions

Questions on (linear or nonlinear) regression, the fitting of functions that best approximate empirical data.

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### Nonlinear Multivariate Regression

Assuming I know exactly my forward model, which is represented by $n$ non-linear functions, or some probability models: $\vec{R}=f(x,y,z)$ , $f:\mathbb{R}^3\to\mathbb{R}^n$ Where each item in $R_i$ ...
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### Minimum required data for cosine fit

With a minimum amount of (noisy) data-points, I need to find the amplitude of a simple cosine $y=A*cos(x)$, where x is an angle from $0$:$2\pi$. I know how to fit data to the function, and I know ...
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### How to find an equation that describes a non-linear correlation of multiple parameters

I tried to search for this problem but I don't know what exactly I'm looking for. I found some empirical parameters that correlate but not linearly. An example follows: $Y_1$ and $Y_2$ are the values ...
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### Derivative of logistic loss function

I am using logistic in classification task. The task equivalents with find $\omega, b$ to minimize loss function: That means we will take derivative of L with respect to $\omega$ and $b$ (assume y ...
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### Exponential curve fit with MATLAB's fit function does not deliver good fit

I am trying to use MATLAB's fit function to fit a curve through a data set which obviously shows an exponential decay. These are the commands I use: ...
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### choose between L1 and L2 normalization in logistic regression regularization

Wondering what are the pros and cons comparing to L1 and L2 normalization in logistic regression regularization part, For example, in below formula, it is use L2 normalization (in squared form of ...
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### This is a question about the best type of regression analysis to use in my software

Let me start by saying that I am not a mathematician and I am not very good at math. I am mainly interested in obtaining the best possible results. I am currently doing trial and error with my ...
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I wanted to implement some penalized regression parameter estimation algorithm by Fan&Li (http://sites.stat.psu.edu/~rli/research/penlike.pdf, section 3.3, [1]), but cannot catch the idea of some ...
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### Force minimum of quadratic fit to certain data point

I want to fit some data $(x_i, y_i)$ with quadratic function. No problem till there. However, I want the polynomium minimum of the fitted curve to be at certain point $(x_k, y_k)$. If it is possible, ...
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### Average Percent Rate of Change

Excuse the png equations, still a MathJax newbie. I am analyzing data I have computed: Alcohol content and Caffeine content retention after a duration of 8 hours for each. I had gotten the data in ...
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### Linear regression from function

I have a function given by its analytical form $f(x,y,z)=0$. Is is possible to calculate linear regression directly from this function on a selected neighborhood of a point? I want to "approximate" ...
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### Least square method

$4$ arbitrary points $(x_1,y_1)$ $(x_2,y_2)$ $(x_3,y_3)$ $(x_4,y_4)$ are given in the $xy$ plane using the method of least squares. If regression of $y$ upon $x$ give the fitted line $y=ax+b$ , and ...
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### How to perform a monotonic function fitting of data points?

I'm seeking suggestions for general purpose function fitting of a set of data points, where, based on physical intuition, the relationship is expected to be "monotonic", i.e. the function should be ...
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### Fast way of finding RSS of Multiple Linear Regression

Is there any smarter way to compute Residual Sum of Squares(RSS) in Multiple Linear Regression other then fitting the model -> find coefficients -> find fitted values -> find residuals -> find norm of ...
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### Linear regression formula derivation

I always thought linear regression was numerically calculated by bruteforcing solutions and comparing them with some $r^2$ error accuracy. However, I recently stumbled upon this formula for ...
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### intuition behind having a unique regression line

I understand this mathematically. we have function of 2 variables represents the sum of square errors. We have to find the $a$ and $b$ that minimize the function. there is only one minimum point. But ...
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