Questions tagged [polynomial]

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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2answers
621 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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Regression: find the best degree of polynomial with the best regularization parameter

When trying to predict data using linear regression or classify with logistic regression, with a polynomial, I know how to find the best degree of a polynomial to fits given data when the ...
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11 views

Expected variance of quadratic regression coefficients with random x-values

I am thinking about a problem where I need to estimate the maximum of a quadratic regression, that is, fit a model $y = ax^2 + bx + c + \epsilon$ and estimate the maximum as $-\hat b/(2\hat a)$. My ...
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Multiple Regression Analysis Beginner

Background: I am using an instrument that measures two physical properties, X1~Temperture and X2~ Velocity. When gathering the data to make the curve a set of predetermined concentrations are chosen ...
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14 views

Obtaining MSE for a smoothing spline model in R

So I've fit a smoothing spline regression model on a training set (code below) and I obtain an 8 digit number as MSE value. When I fit a regular cubic polynomial to the same dataset I obtain a 7 digit ...
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Irreducibility of polynomial in Q [migrated]

I need to prove that : $p(x)=7x^6-35x^4+21x-1$ Is a irreducible polynomial in Q[X] I try Eisenstein , Gauss lemma Modulo p. Thanks in advance.
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1answer
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How do you determine what degree of polynomial to fit to data?

Say you have to fit a polynomial to data that is generated by another polynomial, for example. What is the process of determining what degree polynomial to use to fit that data?
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Squeeze a time series to fit in a range while maintaining shape

I have the following time series with intermediate highs and lows marked by the vertical lines: I want to transform/squeeze the series so that the resulting series would fit in a range, let's say [0,...
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R function `poly` in logistic regression not giving orthogonal results

After reviewing this comment, I have been interested in using the polynomial function within logistic regression. As I understand it, the poly function is useful ...
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1answer
44 views

Polynomial regression seems to give different coefficients depending on Python or R

When I fit a polynomial on the Boston data set with R, I seem to get different results than when I use Python. Example code with R: ...
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1answer
270 views

Training r-squared decreases after adding higher degree polynomial terms to regression model

I was playing around with some examples to get some experience using the PolyFeatures tool from Scikit-Learn, and I ran into something strange. I iteratively added ...
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34 views

Polynomial Regression with too many features

I have a dataset with 10,000 datapoints for every of the 900 features and a target of 10,000 datapoints, so x = (10000, 900) and y = (10000, 1). If I plot the results for the first 100 features on the ...
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1answer
295 views

Fitting a quadratic regression in R

I am trying to fit a quadratic regression model in R. Here is an example of my dataframe: ...
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157 views

If the quadratic term is significant but the linear term is not, we must add the linear term to the model too?

I have a linear mixed effect model and I add the quadratic term of time in my model and it was significant and improve the AIC & BIC of the model, but the problem is that the linear term of time ...
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Singularity issue, caused by polynomial regression, in the wald test of significance

I am trying to explain the housing sales prices and need for it to include the squared terms of some variables, for instance distance to the nearest forest, in order to capture the real effect. This ...
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2answers
259 views

RKHS for polynomial kernel

Say we have a polynomial kernel of degree two: $k(x,x')=\langle x,x' \rangle^2$ for $X=\mathbb{R}^2$. I know that a feature map $\phi(x)=(x_1^2,\sqrt{2}x_1x_2,x_2^2)$ exist. What I want to know is ...
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1answer
128 views

Comparing Polynomial and Linear Model

I have a panel data with unbalanced panel. I am testing a non-linear relationship. I tested a polynomial(quadratic) model for this purpose with following codes in stata. ...
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How to directly know the backward selection model when independent variables are orthogonal?

According to this output, the independent variables are orthogonal. Please tell me, when doing the backward selection, why it can be directly known that it should be reduced to 5th order model?
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Equation for smoothing spline from coefficients?

If I smooth a data vector with a smoothing cubic spline my understanding is that each ‘segment’ between knots should be representable as a cubic polynomial. Is it possible to infer the equation of ...
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Linear regression of higher order polynomial with slope constraint

I am trying to constrain the coefficients on a higher order polynomial (let's say an order 6) for the curve to be decreasing. I have found this link, where the fitting of a 3rd order polynomial is ...
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Fitting data to a sum of correlated polynomials. Can I de-correlate the polynomials?

I have a model that has the form $$f(x; a, b) = (x^2 -M)\cdot a \; +\; (x^4 + M\cdot x^2 + M^2)\cdot b$$ where $M$ for all intents and purposes is known. The domain of the problem is for $x \in \...
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Inflection Point in Quadratic Model

I have a panel data and I am estimating a qudaratic model with fixed effects. The following model is estimated using stata. ...
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5answers
7k views

Raw or orthogonal polynomial regression?

I want to regress a variable $y$ onto $x,x^2,\ldots,x^5$. Should I do this using raw or orthogonal polynomials? I looked at question on the site that deal with these, but I don't really understand ...
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242 views

Why are polynomial activation functions not used

Why are polynomial functions bad as activations?
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79 views

How to interpret higher order polynomial interaction when lower order interaction is significant

I'm having trouble understanding how to interpret the output of polynomial model when the lower order term (linear term) is significant, but the quadratic term is not. For instance, create a random ...
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386 views

Does feature size affect polynomial regression?

By feature size, I mean the value of the numbers. For example, let's say I have input X = [[0],[1],[2],[4]] and output ...
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Changing scale of polynomial regression function [closed]

This is a theoretical question, but I am working on an assignment that gives me a regression formula for wage when compared with years of experience. The regression formula is in the form: $\hat{w} = ...
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1answer
21 views

Finding maximum of quadratic function that depends on other variables

I am trying to fit a model of the following form in R: yield = solar_rad + I(solar_rad ^ 2) where each observation is a field and ...
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1answer
45 views

Opening the linear regression black box

How does LinearRegression fit polynomials? I am not sure why I have to pass to the fit an array of the data where every point has been converted to Nth order ...
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19 views

When to increase the degree of polynomial regression

As I understand it, first we check the pattern of data and if it looks that it is not linear, we try to increase the degree to quadratic.If the curve of the data pattern is more abrupt, the degree of ...
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Is it possible to train an RNN to predict projectile motion?

Projectile motion is given by a function $y = -9.81 x^2 + ax + b$ for some parameters $a$ and $b$. I'll simply assume for $x$ values to be distanced by 1, so $x_t = t$. I can then easily generate ...
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29 views

Time series plots, polynomial coefficients and PCA

I have several time series plots that I have their polynomial coefficients (curve fitting using Matlab polyfit). Is it possible and valid to use Principal Component Analysis (PCA) to try to classify ...
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2answers
42 views

Perfect multicollinearity with a cubic term in the model?

I'm trying to figure out why adding a cubic term in the model doesn't guarantee a perfect multicollinearity. If $X$ is known, then $X^3$ is known in both magnitude and sign and vice versa. It may not ...
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1answer
89 views

Feature selection (backward elimination) in polynomial regression

I have a polynomial multiple (univariate) regression with 2nd degree (for example) as below. Question. When I execute backward elimination to select features, should I remove features from the ...
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Can I transform a few features to polynomial in multi regression?

Let's say I have 3 features in my ols model as below. model = sm.ols(formula='y ~ a + b + c', data=df) Question 1. If I want to transform the feature 'a' as ...
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697 views

What makes linear regression with polynomial features curvy?

The following is my understanding of what happens: if I take a "two dimensional problem" e.g. I have $X$ as inputs and Y as the outcome and I add a feature $x^2$. This gives a problem an additional ...
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1k views

Can you add polynomial terms to multiple linear regression?

I am a little confused about when you should or shouldn't add polynomial terms to a multiple linear regression model. I know polynomials are used to capture the curvature in the data, but it always ...
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1answer
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Questions re. fitting a polynomial: Runge's phenomenon solutions

I have data on hospital treatment times. I would like to fit a polynomial to the data using least-squares. In a previous question raised before I have already been advised against this, but ...
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Can I use polynomial regression with categorical variabels? [closed]

I'm trying to learn a polynomial model of degree 2, but apparently it doesn't work well for dummy variables, as they present only 2 possible values (0 or 1) thus not being able to properly create a ...
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1answer
27 views

Are the following is a good wrap of a comparison between all linear regression types (single, multiple and polynomial)?

I am new to machine learning and it's hard to find an instructor to help you with theory based questions. If this question does not fit to this site feel free to remove it. I am comparing the 3 types ...
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2answers
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Questions re. fitting a polynomial: smoothing, cross-validation, etc

I have data on hospital treatment times. I would like to fit a polynomial to the data. My data comes in 5 minute increments and it is very noisy. It looks like this: I can aggregate to a higher ...
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1answer
348 views

Polynomial contrasts following a one way ANOVA

I have a small dataset that is amenable to trend analysis. Only 1 IV with three levels, a balanced design. Both the linear and quadratic contrasts came back as significant. What would be the ...
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Finding out how change in other variables influence change in target variable

I have data in form of time series that consist 2 variables for 3 different products. First variable is quantity sold and the second is price for each month. And that is repeated for every product. So ...
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Polynomial and simple contrasts for anova

Im wondering if anyone can help me. Im trying to do a 2x16 repeated measures ANOVA with two conditions across 16 timepoints. The main effect of time came out as significant and I was interested in ...
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Why prefer poly() to I() ? Are they different? [duplicate]

A post "Fitting Polynomial Regression in R" used two ways to model the polynomial regression: (a) poly(..., ...); (b) I(...). ...
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1answer
234 views

Including both transformed and original data (untransformed) in a multivariable linear regression.

This may have a quick response (i.e. don't do it). Just attended a lecture on multivariable linear regression where the outcome is forced expiratory volume (the amount of air you can push out of ...
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1answer
353 views

An easy decision when to use a spline or a polynomial

I read a lot about polynomials and splines (and in case of the latter also lots of it derivates) and often some special cases were introduced to explain, mostly, why a spline is more suitable than a ...
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1answer
387 views

What's the inverse of the finite polynomial $\phi_p$ in an $\ ARMA(p,q)$ model?

On learning about ARMA(p,q) models, Box and Jenkins (1970) defined a very important class of stochastic processes that is obtained as a white noise process goes through a linear filter. This can be ...
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What is the best correlation coefficient to use in order to compare how similar two second degree polynomial functions are?

This will likely be a lament question, but then again I am a lament in the area of statistics. Please accept my apologies for that in advance. :) Suppose you have 2 data sets: Dataset 1: some values ...

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