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

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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0answers
84 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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0answers
12 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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0answers
20 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
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2answers
163 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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31 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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47 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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0answers
40 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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0answers
23 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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0answers
25 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
30 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
32 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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0answers
32 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
21 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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0answers
24 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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0answers
20 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
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0answers
56 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
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1answer
48 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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0answers
26 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
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1answer
57 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 ...
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0answers
30 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
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1answer
111 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 ...
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1answer
90 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 ...
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0answers
83 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 ...
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0answers
31 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 & ...
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2answers
175 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 ...
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1answer
39 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
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1answer
82 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
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1answer
44 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 ...
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0answers
25 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 ...
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0answers
66 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 ...
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0answers
107 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 ...
2
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1answer
132 views

Local polynomial regression: Why does the variance increase monotonically in the degree?

How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)? This question has ...
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0answers
41 views

Calculating Polynomial Regression Confidence Bands

I have $N$ samples with known standard deviation: $(x_i, y_i \pm \sigma_i)$. I need to use order-$p$ least-squares polynomial regression to create confidence bands for $\hat y(x)$. I know R can do ...
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0answers
44 views

How to prove consistency of a non constant partial effect

Suppose a data generating process behaves according to the following hypotheses, where for simplicity $x$ is a scalar random variable that enters into the model linearly and through a quadratic term: ...
2
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1answer
223 views

Using B-splines within a linear mixed-effects model in R

I am using linear mixed-effect model (run with the lme() function in the nlme package in R) that has one fixed effect, one ...
0
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0answers
50 views

Comparison of Non-Stationary Time Series Trends

I am trying to compare two readings of the same occurrences from two different sources, forming two time series. I would like to assign a metric to their similarity/dissimilarity, but the method I am ...
6
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4answers
691 views

What are the formulas for exponential, logarithmic, and polynomial trendlines?

In creating linear trendline, I used the following formulas: $$y=mx+b$$ $$m = \frac{n\sum(xy)-\sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y- m \sum x}{n}$$ and this for the R-squared: ...
5
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1answer
61 views

Does a polynomial kernel with degree less than 1 satisfy Mercer's condition

Consider the polynomial kernel: $$K(\boldsymbol{x}, \boldsymbol{x}') = (\boldsymbol{x}^{T} \boldsymbol{x}'+c)^{d}$$ This kernel satisfies the Mercer's theorem/condition. Since I never saw any ...
2
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0answers
46 views

How to determine significance of polynomial?

I'm running a model where both a 2nd or 3rd order polynomial would seem to fit the data. I'm trying to decide which one to use. In the quadratic model (panel fixed effects) the first and second order ...
1
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1answer
171 views

Fractional polynomials vs GAMs

I have been analyzing panel data for a while now using different methods (Generalized Linear Models, fractional polynomials and GAMs). If we just ignore GMMs for now, I have come to find that ...
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0answers
78 views

Polynomial transform of a Gaussian Random Variable

I have been trying to find how the PDF of a polynomial transform of a Gaussian Random Variable could be found. Eg: If \begin{equation} \ X\sim N(\mu,\sigma^2) \end{equation} Then what would be the ...
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1answer
64 views

Reduce the polynomial terms in logistic regression (glm)

I've three categorical variables A, B and C with 5 levels each. The model I'm trying to fit is glm(Y~A+B+C, family=binomial()) How can I remove the higher order ...
1
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1answer
148 views

What is the value of “X” in a regression equation when dealing with a time series?

I am using excel to add a polynomial trend line to a chart. The chart and the formula of the trend line are shown below. I want to add lines indicating different confidence intervals so I need to find ...
0
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0answers
49 views

Should I standardize or rescale with polynomial regression as alternative to difference scores?

I am working with a model that uses polynomial regression combined with response surface modelling as an alternative to difference scores in regression: ...
0
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1answer
79 views

Polynomial regression P value is getting altered

I am running following data and code for analyzing non-linear regression and to get simplest equation of curve that fits the data: ...
1
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0answers
188 views

How to determine if GLM quadratic term should be set up orthogonal or non-orthogonal

I am setting up a GLM in R where I have only one predictor variable and its quadratic form. I understand that in R I have 2 options. ...
2
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2answers
133 views

Maximum Degree of Polynomial Regression

If we have 100 data points and want to perform polynomial regression, the maximum degree of our polynomial is n-1, where n is the number of data points. In this case, the maximum degree would be 99. I ...
3
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1answer
75 views

Changing polynomial degree leads to changing p-values in OLS regression

I have a question about interpreting coefficient $p$-values when fitting a polynomial function with ordinary least squares. When I sequentially fit a linear, then quadratic, then cubic etc. ...
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0answers
33 views

Sample size for validating a prediction model

Dear friends: In an earlier pilot study a third- degree polynomial model was built, X = time (days) Y = Moisture loss. I need to validate this model in a larger study with more samples. ...