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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9 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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15 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
353 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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14 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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34 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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23 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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46 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
108 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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12 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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24 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
28 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
69 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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16 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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35 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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36 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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31 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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36 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
42 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
81 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 ...
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1answer
50 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
33 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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78 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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0answers
36 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
60 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
126 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
328 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) ...
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17 views

What's a good robust approach to something like multi-variable local polynomial regression with known changing noise magnitude?

I have a sample-based estimator of a function $f(x,y)$ parametrized by two inputs. The region of valid $x$ and $y$ is an axis-aligned (bounded) rectangle. I have decided to create a grid of points in ...
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104 views

Problem with R-Squared value

I have a problem to determine my R-Squared value. I do a polynomial regression: fit3 <- lm(value ~ date + I(date^2)+ I(date^3),data=training) I have a R-Squared value (0.9416) when I do ...
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77 views

Polynomial ANCOVA glm in R

I have a data set of success and failure counts with one continuous independent variable and one factorial variable: ...
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52 views

Orthogonal polynomials contrasts for regression (unbalanced)

We can obtain the sum of squares of a contrast for a regression of degree $j$ by: $$ SSR_j=\frac{\left(\displaystyle\sum_{i=1}^{I} C_{ji}T_i\right)^2}{rK_j}, $$ where $I$ is the number of levels of ...
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2answers
368 views

Goodness of fit. How to evaluate if polynomial of order n+1 gives statistically better fit than polynomial of order n?

I fit polynomials with increasing order to some data. What is the best way to evaluate if the additional parameter of polynomial of order n+1 provides a statistically significant better fit than the ...
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60 views

Is polynomial regression restricted to linear models?

I'm wondering if polynomial regression extends to generalized linear models, so one could fit a model with a binomial, Poisson, gamma or other distributions? My question stems from a paper ...
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200 views

Errors-in-variables multivariate polynomial regression (R)

(EDIT: the question has been modified just a little bit to be more specific) I want to fit a multivariate polynomial regression that accounts for measurement errors (an Error-in-Variables model). ...
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70 views

Does feature size affect polynomial regression?

(I'm still trying to learn all this, sorry for any wrong terms or mistakes I might have made in this question) By feature size, I mean the value of the numbers. For example, let's say I have input ...
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36 views

Subtract the mean from panel data?

I'm working with some panel style data and I was wonder if it makes sense to subtract the mean from my predictors as a whole or to do it by year. So lets say I was doing a pooled regression of some ...
2
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39 views

Laurent polynomial regression?

Polynomial regression is a common way of doing curvilinear regression. It is common to also use the inverse transform x^-1 (http://pareonline.net/getvn.asp?v=8&n=6). One can extend the concept ...
3
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1answer
52 views

Backtransforming the vertex of a quadratic function

I have created a model for which it was necessary to scale my predictor values by subtracting by the mean and dividing by the standard deviation of the X values. This resulted in variables centered ...
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1answer
72 views

Interpreting multiple polynomial regression coefficients

I read a couple post on interpreting polynomial coefficients here in cross validate however none of them touch on how to interpret multiple polynomial regression coefficients. Perhaps its the same but ...
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81 views

Polynomial curve fitting and support vector machines

I applied regression using support vector machines and then I approximate the results using polynomial regression and obtain an equation for the results. I applied support vector machines and then ...
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0answers
36 views

glmnet for Mixture Model

I have a distribution that looks like a Gaussian Mixtures And then I use Python's GMM Classification package to cluster them into clusters and then perform glmnet on each of the cluster. Is this ...
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53 views

What does monotone polynomial plot represent?

I am trying to understand monotone and isotonic regression. I believe they will produce curve which are monotonely increasing or decreasing. In most of what I read on the net, the change is shown in a ...
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64 views

Inquiry on comparing quadratic regression models

I am conducting a project in which I am analyzing the relationship between stream flow and algal biomass for a 28 day interval. I have 5 different flow treatments (ranging from low to high flows). I ...
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141 views

3-way interaction with polynomials and 2 categorical variables in a LMER-model in r

My dataset contains the following variables: Within-Subject factor: Target After Onset Prime (4 levels) Within-Subject factor:Prime (2 levels; Categorical) Within-Subject factor:Target (2 levels; ...
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1answer
54 views

What polynomial do I need for regression of such relations

I have following 4 graphs and for each I have to do regression. The relation is clearly curvilinear. What term should I use for regression (eg y ~ x+x^2) for each of these?
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80 views

JAGS equivalent to R's I() (Inhibit Interpretation of Objects) function?

I'm wondering if anyone has come across the JAGS/BUGS equivalent to R's I() function. I am interested in using this in a polynomial logistic regression, i.e.: mod1 <- glm(Employment ~ Density + ...