# 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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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 ...
372 views

### 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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### 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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### 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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### 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,...
33 views

### 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 ...
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: ...
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 ...
30 views

### How to control for binary variables in polynomial regression?

I have a datset: ...
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### 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 ...
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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### 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 ...
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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### 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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### 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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### 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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### 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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### 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 ...
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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### 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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### 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 ...
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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### 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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### 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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### 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 ...
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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### 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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### 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 ...