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

learn more… | top users | synonyms

1
vote
1answer
22 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 ...
0
votes
2answers
41 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? ...
0
votes
1answer
18 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 ...
0
votes
0answers
11 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 ...
1
vote
0answers
24 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 ...
1
vote
0answers
31 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 ...
0
votes
0answers
25 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 ...
0
votes
0answers
18 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.
1
vote
1answer
36 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 ...
1
vote
3answers
53 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 ...
2
votes
1answer
38 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 ...
1
vote
1answer
31 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 ...
0
votes
0answers
33 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. ...
0
votes
0answers
47 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 ...
0
votes
0answers
30 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 ...
0
votes
1answer
51 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: ...
0
votes
1answer
96 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 ...
0
votes
2answers
170 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) ...
0
votes
0answers
16 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 ...
1
vote
0answers
96 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 ...
0
votes
0answers
53 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: ...
1
vote
0answers
39 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 ...
3
votes
2answers
290 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 ...
0
votes
0answers
49 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 ...
1
vote
0answers
134 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). ...
1
vote
0answers
59 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 ...
1
vote
0answers
30 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
votes
0answers
38 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
votes
1answer
44 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 ...
0
votes
1answer
67 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 ...
0
votes
0answers
69 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 ...
0
votes
0answers
29 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 ...
0
votes
0answers
48 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 ...
0
votes
0answers
44 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 ...
0
votes
0answers
113 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; ...
1
vote
1answer
52 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?
0
votes
0answers
62 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 + ...
3
votes
1answer
245 views

Differing significance of linear and quadratic terms

I'm surprised this question has yet to be asked; hopefully it is an embarrassingly simple one. I am fitting a negative binomial regression with 12 total covariates (6 linear variables and 6 ...
1
vote
0answers
47 views

Relationship between Coefficients of Orthogonal Polynomial and Normal regression

So this is more a question to help me understand what is going on rather than application: So in normal regression we have $$ \mathbf{Y=X} \mathbf{\beta} + \varepsilon $$ Now the part that really ...
3
votes
1answer
199 views

Multicollinearity in polynomial regression

How to deal with multicollinearity in polynomial regression? Suppose I have $x$, $x^2$ and $x^3$ as independent variables in my regression equation. How can I calculate and remove multicollinearity ...
1
vote
1answer
107 views

Fit data to a bivariate function

I want to fit my (x,y,z) data points to a function. You can see the data on Fig.1. The data is symmetric along the main diagonal. To understand my data I have studied (y,z) curves at different ...
0
votes
0answers
86 views

Is this polynomial correct?

Disclaimer: I have no knowledge of stats. I fitted a polynomial to data points. I expected it to look like an exponential decreasing curve, but this seems to dip below zero, as well as the histogram ...
0
votes
0answers
35 views

backward shift operator as a sum (heuristic solusion)

I am interested in converting $(1-L)^n$ to a sum, where $L$ is backward shift operator. Let give you an example, \begin{align} \triangle^1 &=X_{i+1}-X_{i}\\ \triangle^2 & ...
5
votes
2answers
223 views

What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomial regression?

Say we have a Bayesian polynomial regression like the following. $$y_i \sim N(\mu_i, \sigma^2)$$ $$\mu_i = \beta_0 + \beta_1 x_i + \beta_2 x_i^2 + \beta_3 x_i^3 $$ where $x_i$ is some mean centred ...
1
vote
1answer
42 views

Regression against polynomials and log-linear predictors

I have a regression problem where one of the predictors has a very good fit as $Y \sim poly(X_1, 2)$. However, $Y$ is clearly log-linear against my second predictor $X_2$, so $ln(Y) \sim ln(X_2)$. ...
3
votes
1answer
135 views

Stability of univariate fractional polynomial models

I can't decide what is the best way to assess the stability of a higher order fractional polynomial model. To use an example I have been working on, I am analyzing a dataset with panel data selected ...
1
vote
1answer
58 views

Sign changes when I cube a variable in a linear model

In my linear model I have the variable of interest $x$, and a whole bunch of covariates that I condition on. The coefficient is significant and positive. I have reason to believe that the connection ...
0
votes
0answers
26 views

Comparing difference between two polynomial regression models in R [duplicate]

I've been having some trouble in attempting to compare sets of data. I can't seem to analyse whether two models describe the same set of data, or if they describe different sets. Here is my a portion ...
1
vote
0answers
109 views

How to perform a regression with orthogonal polynomials (such as laguerre) in R? [closed]

Using R software, I'm trying to perform a polynomial regression on E(Y|X1, X2, X3). In fact, E(Y|X1, X2, X3)must ne equal to a linear combination of polynomial with orthogonal basis (such as Laguerre ...
1
vote
0answers
153 views

Significant turning points in fractional polynomials

When using fractional polynomial models it has been suggested to use the first derivative of the polynomial function to identify significant periods of change and the second derivative to identify ...