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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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10 views

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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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
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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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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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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 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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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
26 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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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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327 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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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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R - Interpretation of coefficients and written form of fitted model in lm() linear regression when using poly()

I've tried reading several resources on poly(), I'm not able to see an answer to my question. My question pertains how I might present my fitted linear model in a way that the coefficients are ...
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Poly() function in R for linear models

I am working with some data on which I used the poly() function to get 4th degree polynomials. I had one model that only had significance for the first degree, so I ...
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21 views

Polynomial Regression with grouped independent observations

I am trying to model how porosity changes across burn up levels of a fuel pellet. I have 300 observations at varying levels of burn up. The way my data is collected makes burn up appear as a ...
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1answer
55 views

How to explain the result of this polynomial equation?

Lets say that I predicted plant productivity (logy) by precipitation (logx1) and moisture content of soil (logx2). my original data gives me the best result only after taking logarithm on both side of ...
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1answer
29 views

Is it ok to use polynomial model to fit logarithmically transformed data?

Can we use polynomial regression using logarithmically transformed data. I transformed both y and x1 and x2 variables by natural log. After this, I used polynomial regression to fit. when using poly(...
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1answer
46 views

Why are polynomial activation functions not used

Why are polynomial functions bad as activations?
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1answer
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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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1answer
69 views

Choosing a significance test, trend appears either linear or quadratic

I am testing a one-sided hypothesis of association between two variables. I want to know if I increase variable A, then will variable B also increase? For my experimental design, I increase the ...
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Response surface analysis and simple slope analysis - contradicting results

I performed a multi-level polynomial regression (two IVs, one DV) with some control variables, and also computed the response surface coefficients a1 to a4 alongside simple slope coefficients (+/- ...
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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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45 views

Polynomial regression in a circular data set

I'm working on a data set where I have a set of events per time of the day (in a 1h time slot). I made the sum of the events and plotted a bar as show below. In order to define an equation that could ...
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Polynomial Regression model fits poorly

I was reading ISLR and implemented the least squares approach for a linear regression model on the autos data set which comes with the book. For the least squares approach I used only one predictor(...
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1answer
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How can I use polynomial distributed lag models for longitudinal categorical exposure?

I have SHS data from 13 time points and i want to describe the relationship between this cumulative exposure and health outcome after the 13th time point. It seems the ...
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64 views

Calculating predicted value from polynomial regression by hand

I have the following output from from R. I know we can calculate predicted values using the predict() function. How can we calculate the predicted value by hand if X=2 or 3? I'm using the below ...
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Unclear “mathematical notation” in a polynomial

Although, the Enigma here is a protocol for enhancing the privacy in blockchain; however, the question is about mathematical notation, where we want to calculate the coefficients in a polynomial. ...
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1answer
32 views

ANCOVA with Polynomial Categorical Variable

I have a homework problem that asks me to fit a one way ANCOVA model to a set of data (which I feel comfortable with). The model is represented as yij = μi + γzij + eij where i indicates ...
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1answer
124 views

Using a given polynomial formula in a lm() model in R

I am currently trying to fit a polynomial model to measurement data using the lm() function. fit_poly4 <- lm(y ~ poly(x, degree = 4, raw = T), weights = w) ...
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19 views

Package to perform 2nd degree polynomial regression with L1 penalty for use of the 2nd degree

I'm trying to fit either a straight line or 2nd degree polynomial through many sets of points (2-dimensional data). I would much prefer a straight line over a polynomial, so am trying to penalize the ...
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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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21 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
64 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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68 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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47 views

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
141 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
101 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
59 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
86 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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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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31 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
81 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
223 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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139 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
140 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
160 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 ...