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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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18 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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0answers
15 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
26 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
18 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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23 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
44 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
27 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
24 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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0answers
8 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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0answers
44 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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0answers
12 views

Correct classification of function of four-point trajectory

This graph depicts the output of group-based trajectory modelling (generated using the 'traj' plug-in in STATA). Strangely, the model has the highest AIC when all three trajectories are defined as ...
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0answers
16 views

The predictive error with the degree of the polynomial kernel?

For kernel SVM, I figured that predictive error getting bigger with the degree of the polynomial kernel goes higher. Does anyone know why is that?
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0answers
19 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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46 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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0answers
44 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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0answers
26 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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50 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
23 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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0answers
7 views

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
12 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
96 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. ...
2
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1answer
55 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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0answers
32 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
46 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
86 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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0answers
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
14 views

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
111 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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0answers
17 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
38 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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0answers
26 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
956 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
472 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
94 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
32 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
132 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
96 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
49 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
31 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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0answers
49 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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0answers
78 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
350 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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0answers
21 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 ...
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0answers
63 views

When to use Linear Regression against Polynomial Linear Regression and vice versa

How can we decide upon when should we take up Linear Regression as against Polynomial Linear Regression and vice versa? What can be some use cases that justify the use of each concept and clearly ...
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0answers
408 views

How to report results of a polynomial regression with a discrete independent variable

I have been recently trying to fit a linear model to my data. The dependent variable is continuous and the independent variable is numeric and discrete. When I first test the assumptions concerning ...
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0answers
30 views

Polynomial model selection of benchmark data in R

I have run a set of benchmarks where I changed one parameter at once, let's call it p, and its value in each run n. I measured <...
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0answers
133 views

Identify important interactions terms in SVM with polynomial kernel

I have an SVM model with polynomial kernel. I have output of feature weights, but they are all the individual features. Is there a way to know which interactions between individual features are most ...
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1answer
57 views

Functional form of binary independent variable

I am considering a model with a dummy variable on the right hand side. The dummy variable takes the value 1 when an underlying continuous variable is greater than some threshold and zero otherwise. ...
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1answer
213 views

Is polynomial regression possible in H2O? [closed]

Is there a way to carry out polynomial regression $x + x^2$ in H2O (Python)? What I have found about this is "interactions" option in GLM. However, I am not sure if this option yields polynomial ...
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1answer
277 views

Comparing difference between polynomial and linear regression (accumulation curves)

I have accumulation data and curve for two drugs, one follows linear regression, whereas the other may be described with polynomial model. (See the attached figure.) What is the correct method to ...