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.
0
votes
0answers
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
0answers
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
1
vote
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 ...
2
votes
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 ...
0
votes
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 ...
0
votes
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?
1
vote
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, ...
1
vote
0answers
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 ...
1
vote
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 ...
1
vote
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 ...
0
votes
0answers
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
...
2
votes
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 ...
0
votes
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 ...
1
vote
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 ...
1
vote
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
votes
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 ?
0
votes
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 ...
0
votes
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 ...
2
votes
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
...
0
votes
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 ...
2
votes
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 ...
1
vote
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 ...
1
vote
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 ...
3
votes
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 ...
0
votes
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)
...
4
votes
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?
0
votes
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 ...
4
votes
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 ...
1
vote
1answer
32 views
Interpretation of Significance in a Polynomial Model?
I have the following output from a polynomial regression summary in R:
...
0
votes
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 ...
2
votes
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 ...
0
votes
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 + ...
0
votes
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 ...
1
vote
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 $Cov(z_t, e_t)=0$.
...
1
vote
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 <...
1
vote
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 ...
1
vote
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. ...
2
votes
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 ...
0
votes
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 ...
