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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31 views

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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1answer
17 views

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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13 views

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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14 views

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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24 views

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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14 views

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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5 views

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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1answer
24 views

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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5 views

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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14 views

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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65 views

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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1answer
37 views

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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1answer
11 views

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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1answer
99 views

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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2answers
130 views

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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1answer
31 views

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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1answer
55 views

Nonlinear Regression with linear method from Python's scikit-learn/ sklearn using a polynom

I am trying to do a regression analysis for some data, say 20 variables $\left( {{x_1},{x_2},{x_3},...} \right)$ where the underlying probability distribution is known (e. g. ${x_1} \in {\rm N}({\mu ...
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35 views

OLS, phenomenon { alpha = - mean(beta_2*x_orig)} : coincidence?

as suggested in the title, when with some data I perform this model: y ~ alpha + beta_1 * x_1 + beta_2 * (x_1)^2 + error term with OLS I SOMETIMES fall into the ...
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4answers
156 views

Something wrong with my implementation of the bias/variance diagnostic in polynomial regression

I'm trying to diagnosing bias/variance so I have the below Octavecode: ...
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16 views

Polynomial curve fitting for temperature prediction

First of all, I would like to say that I know very little about statistics. I need to make a C# application to predict three days weather for school project and need some model and have been exploring ...
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36 views

Intuition behind the characteristic equation of an AR or MA process

Ok, so I've just started learning Time Series Analysis. We can write an MA(q) process as Yt = θ(L) ϵt and an AR(p) process as ϵt = φ(L) Yt in terms of the lag operator. Then, with no explanation (...
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1answer
376 views

Distribution of a second degree polynomial of a Gaussian random variable

I would like to compute $$P(Y=aX^2+bX+c<0)$$ where $X \sim N(0,\sigma)$. I can do it quite easily using Monte Carlo. However, I've been asked to find the analytical pdf $f_Y(y)$ of $Y$ and then ...
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19 views

Power analysis for polynomial regression

There are two variables, $X$ and $Y$. I am interested in the shape of the relationship between $X$ and $Y$, specifically whether it is linear, curved, or some higher order polynomial function, because ...
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37 views

How to calculate the Variance of a linear combination with dependent sums and products?

For my research it is necessary to calculate the significance of the following coefficients: a1=b1+b2+(b7+b8)*W a2=b3+b4+b5+(b9+b10+b11)*W a3=b1-b2+(b7-b8)*W a4=b3-b4+b5+(b9-b10+b11)*W. They are ...
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34 views

Confidence intervals on the derivative of a polynomial surface

My problem is the following: I have fit a surface to some xyz coordinate data to obtain a polynomial surface. That's a polynomial in the variables x and y giving a surface of z-values. I know how to ...
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48 views

Stationarity in the Almon lag model

I have a quick question regarding the Almon approach (Shirley Almon) as presented in chapter 17 of Gujarati's Basic Econometrics. In an example given in the textbook, they use non-stationary data ...
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13 views

how to get polynomial equation for given data in regression analysis? [duplicate]

I have following data and I want apply regression analysis for this data.Based on the data I want derive equation of 2nd or 3rd or 4th order polynomial equation. How can I do that by using math ...
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14 views

Polynomial features on logistic regression [duplicate]

I'm working on a LR model, I'm currently trying to add some polynomial features of degree 2. Since the next step is choosing which polynomial features I have to discard, I've got a question: if I keep ...
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2answers
134 views

Quadratic terms in logistic regression

I am looking at the results of a logistic regression model (i dont have the data) and the person who has developed the model has included quadratic terms in the model. I understand the use of such ...
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15 views

Interpolate from curve data

I have these curves, From this curve I can determine the life of a prop shaft due to gyroscopic forces at different yaw angles and certain speeds. I performed curve fitting on data points to get ...
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0answers
14 views

Results from fractional polynomial models

I am using multivariable fractional polynomials to evaluate several continuous variables in a Cox proportional hazards model. I have the beta coefficients, however, I would like to estimate the hazard ...
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34 views

Back transformed slope of a polynomial regression when the response is logged?

I’m currently analysing some ecological data with R using the following regression: lm(log(y)~x+I(x^2)) As I’m a newbie to modelling I’m wondering now if it’s okay to use a log transformation and a ...
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1answer
34 views

How to explain simply that the set of runs for Non Intrusive Polynomial Chaos cannot be used as a Monte Carlo sample

I had quite an annoying problem at work, a few days ago. I was doing a forward Uncertainty Quantification analysis using Non Intrusive Polynomial Chaos (NISP) (see for example here). Basically, you ...
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2answers
93 views

is linear regression/polynomial regression sensitive to irrelevant features/noise

is linear regression/polynomial regression sensitive to irrelevant features/noise will their respective weights/coefficients be automatically be tuned down? or is it a straight nail in the coffin? ...
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1answer
20 views

Justify choice of polynomia based on statistically significant result?

I am using an OLS. The variable of interest is Nth day to the end of the year (discrete variable). I would like to represent the relationship between y and Nth day to the end of the year with a ...
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24 views

Orthogonal polynomial coding

Is there a "formal" interpretation of parameters associated to orthogonal polynomial columns when having a regression on ordered categorical variables? I mean: you can interpret the $\beta_j$ as $E[Y |...
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41 views

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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38 views

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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36 views

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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51 views

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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1answer
48 views

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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3answers
104 views

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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1answer
59 views

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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1answer
34 views

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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37 views

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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112 views

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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39 views

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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1answer
67 views

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: ...
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1answer
145 views

Linear Ridge not correct prediction/coefficients- Scikit learn

I am using a similar code to this ridge example. The code proposed is simple. X and Y points inside [-1,1] range and predict the radius creating polynomial features and ridge linear regression. As ...
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2answers
507 views

Response Surface Methodology (RSM) for A Mathematical Model

I would like to create a second order polynomial model using Response Surface Methodology (RSM) for a non-polynomial mathematical model. For example, I would like to represent $f(x)=x_1 + \sin(x_1x_2) ...