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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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test for moderation in a quadratic regression model

I am trying to test for moderation in a quadratic regression model. my results show significant evidence of a quadratic relationship on one of the independent variables (x1) and also significant ...
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15 views

How to automatically identify degree of multiple independent variables of Polynomial Regression in R

In the dataset, there are 8 independent variable and 1 dependent variable. I want to use polynomial regression to find the relationship between independent variables and the dependent variable. The ...
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1answer
33 views

Quadratic polynomial - how to test correlation between x and y?

I have one dependent variable (fish abundance) and one independet variable (time), both continuous. I would like to test the correlation between them because I expect that the abudance changes over ...
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26 views

Explanation of covariance matrix of polynomial parameters [duplicate]

I'm asked to find the covariance matrix of $\alpha$, $\beta$, and $\gamma$ for: $$y_i=\alpha+\beta(x_i-\bar{x})+\gamma[(x_i-\bar{x})^2-\zeta^2]+\epsilon_i$$ where all the errors have equal variance $...
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Plot confidence interval of average polynomial fit from coefficients

I am studying the propagation of a wave and to do that I want to follow the position of my maxima over time. In order to do that I thought to fit a polynomial on the data of each replicate, then save ...
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1answer
39 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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2answers
39 views

Can polynomial regression be used to handle data with more than one dimension?

Polynomial regression is said to be a subclass of linear regression. However, it seems that only linear regression can handle data input with more than one dimension, whereas polynomial regression ...
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1answer
43 views

Difficulty fitting polynomial model to data

I need to fit a model to an existing dataset such that I can use the parameters to replicate the best-fit curve to manage the behaviour of an application. I've been trying to fit a polynomial model, ...
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1answer
60 views

Orthogonal polynomials with respect to weighted inner product

Recently I have posted a question on SO, but maybe here is better place to ask. So, I have data and I want to fit polynomial of order $k$ orthogonal with respect to weighted inner product of functions:...
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23 views

What is the consequence from building polynomial regression with multiple ind. variables?

I'm exploring polynomial regression. I understand how to execute it for cases with one independent variable. What about cases with multiple independent variables? I'm working with the boston housing ...
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22 views

Selection optimum polynomial fit

I have fitted polynomial model of orders 1-4. I have three predictors with 7 levels and my response is 400 values from 0.6-0.9, which seems to be bad for information criterions. I am interested in ...
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2answers
46 views

Interpreting linear and polynomial predictors in LMM

I am using linear mixed models to investigate change over time on the score on a questionnaire, which was administered at 5 points in time. While I hypothesized a decline, I had no a priori ...
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1answer
43 views

Catboost Regression. Function Extrapolation

I'm new at ML and have a problem with catboost. So, I want to predict function value (For example cos | sin etc.). I went over everything but my prediction is always straight line Is it possible and ...
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44 views

Fitting multiple polynomial regression

I hope someone could advise to interpret and report outputs of the multiple polynomial regression fit. I am trying to do a simple sensitivity analysis of an empirical threshold-based ecological model ...
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1answer
56 views

Polynomial regression with multilevel data

I want to estimate a polynomial regression to test the effect of self and follower-perception of leadership behavior on some outcome (e.g., followers' job satisfaction). Hence, I have a multilevel ...
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1answer
59 views

polynomial regression in R: how to add hard constraints (go through specified points)? [duplicate]

I'd like to perform polynomial regression on my data (which lies in [0,10]), but I need to ensure that the endpoints of the range are fixed, i.e. that the curve goes through (0,0) and (10,10). So the ...
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1answer
33 views

Relation between number of features, higher order polynomial features and overfitting

Recently I came across an information stating that, if we have too many features, the model is most likely to overfit. I not sure why exactly this is happening. I mean, if I don’t use any higher order ...
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9 views

Difference in Predicted output in polynomial regression [closed]

In polynomial regression when the coefficients applied to calculate the predicted values manually is different from the output generated from the software. How to get the correct predicted values ...
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47 views

why not chosing always a spline?

I'm having a quite simple question: Why is a spline fit not the best choice everytime? In other words: How do I separate a spline fit from a kernel smoother or a polynomial in a meaningful way? I'm ...
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31 views

Polynomial chaos expansion and ODEs

I am trying to figure out how to use PCE. My background is dynamics and analysis. So if I understand correctly the main idea is that we have a random variable $X$, whose distribution we do not know, ...
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64 views

Linear Regression - Which Features Should We Apply a Polynomial Transform to and Why? [closed]

In which situations would a feature have a polynomial transformation appropriately applied to it, and why would we do this; what ultimate impact does this have on the data. Supposing we select the ...
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70 views

how to visualize the graph use matplotlib on polynomial and multiple regression with multiple predictors

Multiple: y=b0+b1X1+b2X2+b3X3....bnXn Polynomial: y=b0+b1X+b2(X)^2+....bn(X)^n Step1: Importing package import pandas as pd import numpy as np import sklearn import matplotlib.pyplot as plt import ...
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27 views

How to get specific terms of a polynomial function in a regression?

I want to simplify data from a complex modell like: fit <- lm(z ~ poly(a,4)*poly(b,5)*poly(c,6), data = somewhat) As I don't know which terms of the complete ...
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70 views

How to manually compute response variable using regression with poly [duplicate]

I believe I can manually compute response values from coefficients obtained using 'raw' polynomial predictor variables. Example R code is ...
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2answers
26 views

Maximum degree of a polynomial trend model

I have read some answers saying to make the maximum degree equals n-1 for testing. However, I wonder if it is also the case for a polynomial trend model with season variables included. I am using ...
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Determining Polynomial Trend, Stationarity, and Covariance of a Process

I'm given $$ Y_t = p(t) + \epsilon_t $$ where $\epsilon_t$ is a stationary series with covariance $\gamma_t$. Also given $$ p(t) = \sum_{r=0}^kK_rt^r $$ where the $K$s are constants, for the ...
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1answer
19 views

Does it make sense to do a polynomial contrast on a continuous time variable?

I tried running a few polynomial contrasts in SAS for a continuous time variable for linear, quadratic, cubic and quartic contrasts and the F values for each were the same. When I used categorical ...
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1answer
105 views

What more advanced methods can I use to predict future sales other than polynomial fitting? [closed]

I am using the polynomial fitting method to forecast the sales of a product throughout different years, where the polynomial is of degree 1. The error is measured by the sum of the squared residuals. ...
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1answer
59 views

How to check if a polynomial regression has any predictive value? [closed]

After fitting the polynomial data to a given curve, how can I check which of the many curves has the most predictive value ?
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34 views

Compare models with robust methds - R

This question is the first part of a larger question that is continued here. I thought that it could be easier to split it into two questions to generate better answer to both and to help further ...
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2answers
52 views

Compression of 18000 curves

I have over $18000$ curves that I need to compress to save $\geq 50\%$ of space. Each curve is described by points $f(1), f(2), ..., f(96)$, each $f(x)$ is 8-bit long. The curves in compressed form ...
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2answers
87 views

What kind of forecasting model for this curve?

I have two years of data - I want to forecast how the 2nd year of traffic will behave based off the previous year of data. The x axis is time, where left -> right is moving forward in calendar year ...
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16 views

Sensitivity study: measuring the effects of free parameters on performance measures of simulation

I am running a series of computer simulations in which I am outputting several performance measures. I want to know how much of the variability of these measures is due to the free parameters of the ...
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1answer
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Distribution of a dice pool [duplicate]

The article Three Basic Distributions from AnyDice shows the distributions (and cumulative distributions) of 1d10, 2d10 and 3d10. Looking at the graphs, it seems there is a pattern here: 1d10: the ...
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1answer
181 views

forward model selection on multivariate polynomial regression with high dimension data

I am trying to fit the best multivariate polynomial on a dataset using stepAIC(). My problem is that I have more variables (p=3003) than observations (n=500), so ...
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21 views

How do factorization machines work for degree 3?

I understand that factorization machines as polynomial regressions, but their second degree coefficient form a matrix that is factorized as two smaller matrices. Some approaches for higher-order ...
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1answer
68 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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27 views

Type of regression for a mix dataset

I am building a model for the following TYPE of dataset: Target function has float numerical values Variables are: 2 variables are float values 4 other variables are integers (Yes/No = 1 or 0) ...
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1answer
1k views

When is it better to use Multiple Linear Regression instead of Polynomial Regression?

In the course I've just learnt Multiple Linear Regression and Polynomial Regression. Why would you ever use Multiple Linear Regression when Polynomial Regression will always fit the data better?
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1answer
735 views

Degree Parameter for SVM Polynomial Kernel

For Support Vector Machines, what effect does the degree parameter have on a model, when using a polynomial kernel? I was able to find an intuitive explanation of the influence of cost and gamma ...
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1answer
136 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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1answer
36 views

Interpretation of Significance in a Polynomial Model?

I have the following output from a polynomial regression summary in R: ...
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2answers
234 views

Why does Mean Square Error decreases when I fit higher degree of polynomial?

I understand the intuition of polynomial regression with higher degree are able to fit the data better, as it is able to decrease your bias but increases the variance. However, I am unable to proof ...
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1answer
135 views

Model stability and variability

I am using polynomial regression to predict mean occupancy in a hospital unit using average length of stay (LOS) and arrival rate to the unit. I am using different percentages of training sets to ...
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0answers
57 views

Deriving bias from misspecified functional form

I am trying to derive the bias from omitting a quadratic term if the true model is indeed quadratic. For example, suppose I estimate: $y_t = b_0 + b_1x_t + e_t$ But the true model is: $y_t = b_0 + ...
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1answer
35 views

Quadratic Association

I am looking for the best way to depict a concave, quadratic association. I'm using logistic regression to measure the association between affect and military advancement (yes/no). The primary ...
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58 views

Instrumental Variable Polynomial Regression

Consider the following polynomial regression: $y_t = b_0 + b_1x_t + b_2x^2_t + e_t$ where $x_t$ is endogenous but there is an instrument that satisfies $Cov(z_t, x_t,)\ne0$ and $Cov(z_t, e_t)=0$. ...
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96 views

Calculate the 'economic significance' of a quadratic term?

I am calculating the "substantive significance" of my most important independent variable in my logistic regression. Using a simulation to assess the strength of my independent variable for my ...
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1answer
393 views

Calculate R2 score of a fitted polynomial regression curve whereby one x point has multiple y-true values

How do I calulate the R2 score of a fitted polynomial regression curve whereby one x point has multiple true y-values? The sklearn r2_score(ytrue, ypred) method ...
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22 views

2nd degree polynome instead of restricted cubic splines

I am looking for an alternative to restricted cubic splines, which can provide a numerical result that is easier to interpret and compare (as far as I understand, this is not easily possible with ...