# Tagged Questions

A mathematical expression w/ >1 term containing the same variable (eg, x & x^2). Polynomials are commonly used to model curvilinear relationships.

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### Orthogonal polynomial expansion and QR decomposition

Here is the source code of R poly function (boundary checking are removed). Why we can use QR to build polynomial expansion, ...
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### How to extrapolate this simple trend line into the future for the purpose of forecasting in Matlab?

We have the following data points in variable data pertaining to a problem that we are solving: ...
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### Selecting polynomial terms in regression

I'm developing a nonlinear response correction for a sensor (to transform "raw.peak" to "target"). I don't care about interpretability. I do care about future accuracy. One might first just throw it ...
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### Choosing polynomial expansion complexity [duplicate]

Here's a specific question I haven't seen asked/answered. Motivation: if you're doing linear regression of two terms plus their interaction, and only the interaction is significant, you keep the ...
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### Multivariate orthogonal polynomial regression: Polynomial basis functions

Consider the following data-fitting problem: $$\min_{\beta_{\tau}}\sum_{i}\rho_{\tau}(y_{i}-\beta_{\tau}'f(x_{i},z_{i},\eta_{i}))$$ where $\rho_{\tau}(u)=u(\tau-I(u<0))$ is the piece-wise linear ...
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### Comparison: Exponential Regression vs Quadratic Polynomial Regression

See this file here: Decay.TXT. I first tried to fit the logarithmic model first ...
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### logistic regression multivariable fractional ploynomials stata vs. R

I a going through Hosmer, Lemenshow and Sturdivant's (HLS) Applied Logistic Regression (2013) and trying to interpret the difference between what STATA is doing and what R is doing. Concerning the fit ...
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### Comparing two models through ANOVA with different types of functions

See this file here: Decay.TXT. I first tried to fit the logarithmic model first ...
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### Naive Bayes predicting on which golf course a player is going to play on today

Similarly to the famous golf course scenario, how would apply Naive Bayes if you had to predict on which golf course a player would play on?(Rather than play or not play) For example, if the dataset ...
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### Method for stochastic data partitioning

I have one task. I have random polynomial like $F(x) = a_0(\omega) + a_1(\omega)x +\cdots+ a_n(\omega)x^n$, where $a_i(\omega)$ is a random variable for each $i = 1, \ldots, n$. Let looks for a ...
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### predict function over or underestimates in cases where polynomials are included in lmer (and glmer) models

I have been having trouble with the predict function underestimating (or overestimating) the predictions from an lmer model with some polynomials. Hopefully my edits make it clearer. I have scaled ...
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### What is the name of figure where the fitted curve becomes the straight center line (figure in description)?

There's a figure attached to this post. The left hand side of the figure shows a graph with a polynomial fitting the data. The right hand side shows the same data plotted on a different scale but ...
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### Kernel feature mapping: Derivation of polynomial kernel

The question is related to the derivation shown in section 3.1 Examples in the following lecture: http://people.eecs.berkeley.edu/~jordan/courses/281B-spring04/lectures/lec4.pdf I am confused about ...
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### Linear regression polynomial slope constraint in R

My problem is how to find the best decreasing 3rd degree polynomial regression in R. I have data, lets say ...
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### Is there a black box that can extract polynomial (quadratic) relationships?

I have an equation of the form $f(x)=\alpha x + \beta x^2$ that I want to match to experimental data. My current approach is to plot the data on a log-log scale and find the slope unity region (by '...
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### How to translate orthogonal polynomial parameters back to the original metric

I am trying to work out how the parameters from a lmer model using orthogonal polynomials can be translated back to their original metric. Chapter 5.3.3 in Hedeker, Donald, and Robert D. Gibbons. ...
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### Can a SVM with polynomial kernel lead to overfitting?

I'm currently searching for the best set of parameters for a Polynomial Kernel with a grid search. I would like to know if using a high value for Polynomial order (10, 100 or 1000) can lead to ...
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### Predictive validity question using cubic linear models R

I have a data set with 2 months worth of observations from one of our clients, 1 observation per day. I am trying to predict number of sales based on two expenditure methods. My independent variables ...
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### Multiple regression / fitting with Legendre polynoms in R

I have to fit a Y data with 14 risk factors X with Legendre, Chebyshev and Laguerre Polynoms. Each variable has 25000 elements and X is the design matrix. At first I had to fit with ...
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### How does a curve fit accuracy depend on the number of points?

The accuracy of a curve fit must increase with the number of points (perhaps like sqrt(N)), but I haven't found an equation for it. Trying estimate accuracy of a 2nd order poly fit. Thanks.
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### Centering variables in regression leads to the same model of original variables, why still doing that?

The regression model y= b0+ b1 x + b2 x^2 + b3 x^3 and the second regression model y = b0 +b1 (x-u) + b2 (x-u)^2 + b3 (x-u)^3 where u is the mean of x These two models lead to the same curves, or ...
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### Best basis set for polynomial expansion

I want to do a regression of x onto y: $$f(y)=c_{1}x+c_{2}x^{2}+c_{3}x^{3}\cdots$$ Obviously a plain Taylor expansion as above is suboptimal since the coefficients will not be orthogonal/...
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### Logistic Regression - Adding a polynomial basis to my input matrix make sense?

When I tried to run logistic regression on a 1500 X 35 input matrix, I obtained an error of 0.23 with 0 -1 loss. Then, I tried to add a polynomial basis of degree 2 or 3 to my matrix, which can be ...
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### polynomial regression: what do large values of Y mean?

I have a time series of x:libor and y:money rates. using the following polynomial y=b0+b1(x)+b2(x)^2, i get values of y that exceed (or are sometimes negative) the coveriance/variance for large ...
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### How to compare future data sets to a baseline

I'm trying to find a way to compare future data sets to a fixed number of unique control data sets. The goal is to use the control data sets to determine which system is likely generating the data. ...
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### Fitting a covariate without the intercept GLM R

I'm trying to fit polynomials without the intercept terms, i've run the following. The first line works but it includes an intercept term ...
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### Random coefficients in regression

Can I use the random coefficients extracted from a random coefficient growth model as predictors in a regression analysis? If the random coefficient growth model also contains a second-order ...
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### Regression plot and function for: heavy-tailed probability distribution

I've got data points from a simulation as coordinates in a text-files like so: ...