# 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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### Polynomial contrasts statment in SAS [closed]

I want to make a polynomial (linear, quadratic and cubic) contrast statement in SAS. I have four levels of treatment, and they are unequal. How can I make the contrast statement? Kindly guide
1 vote
27 views

### If there are cubic polynomial features, then isn't this a polynomial regression, not a linear regression? [duplicate]

I have the following problem: Consider a Linear Regression problem with two features. Based on your visualisation of these 2D features, $x_1$ and $x_2$, on the training set, you noticed that using ...
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### Normality of residuals versus AIC and "best" fit

Hoping to get some insight into normality of residuals vs the "best" fit of the model. After running a simple linear regression and checking normality of the residuals, I logged my outcome ...
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### Optimisation of Polynomial Fittting Process

I have built a multitvariate log link GLM model and I want to fit polynomials to some of the numerical variates (i.e. fit polynomials of order 1,2,3 etc to the relativities of the model). However, I ...
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1 vote
27 views

### Propensity matching affects significance of polynomial degrees differently

I have a regression as follows: $$y = \alpha + \mu L + \beta_1 x + \beta_2 x^2 + \varepsilon$$ where L is a dummy, and x is a control variable. Both $x$ and $x^2$ are significant when I run the ...
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1 vote
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### How to convert B-Spline to piecewise polynomials?

Suppose I have a basis spline $$S(x) = \sum\limits_i N_{i,k} a_i$$ defined on the interval $x \in [a,b]$ with control points $a_i$, degree $k$. $N_i$ are the basis spline functions. The knot vector ...
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### Model converges when using orthogonal polynomials but fails to converge when using raw polynomials

I am fitting linear mixed effect models with random slopes (lmer4 package), and I recently attempted to add a quadratic term due to some theory behind (the quadratic ends up also in the random slopes, ...
17 views

### Polynomial fitting from robust linear mixed effects model

I have run a robust linear mixed effects model to determine the standard deviation within subjects for a repeatability study on a new imaging device. The SDw was derived from the square root of the ...
115 views

### Fitting regression where data is concentrated at the origin

I'm doing an exploratory data analysis which is looking at a number of character-level features of Chinese writing. The association I am looking at currently is that between the complexity of the ...
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1 vote
95 views

### Orthogonal or Raw Polynomial regression?

I am carrying out an analysis where I want to test for a relationship between two biological variables. The response is proportional (so I'm using a binomial GLM with weights) and the explanatory ...
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### If you drop the "1-" in the formula of R2 and calculate the adjusted R2, does that metric mean anything?

First off, sorry for the convoluted title, but I didn't manage to come up with a shorter one. Background: I have some 2D particle tracks that I would like to fit with polynomials. The tracks are ...
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### Polynomial regression with multiple independent variables

I have data set with 3 indepdent variables and 1 dependent variable. They are related to each other in the following way. y* = a q^{1/3} + b q R C_{NS} + c where a,...
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### Orthogonal polynomial contrasts in SPSS (for a binary logistic regression)

I have 4 IVs: gender (male, female), marital status (married, single), threat (continuous variable) and stress with four levels (ranging from 7 to 10 with ten being 'most stressed'). My DV is ...
34 views

### Is polynomial interpolation with RKHS in some way more advantageous than simple Lagrange interpolation?

The reproducing kernel Hilbert space associated with the polynomial kernel $K(x,z)=(1+xz)^{d-1}$ (or other similar polynomials) can be used to interpolate a continuous function $f$ at by its value at ...
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### Should You Specify a Curvilinear/Non-Linear Effect If You Suspect It is Spurious?

Consider the following (simplified) example of a project I am working on: I assume that $X$ has a linear effect on $Y$. However, after plotting the relationship on a scatter plot, it looks like the ...
1 vote
77 views

### Compare quadratic coefficients between group levels from mixed effects model?

I'm hoping I can find some advice on this question. I have repeated measures of an outcome variable yvar where the trend over ...
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### Interpreting linear and quadratic terms with same sign

I am running a second order model with betweenness centrality and closeness centrality as independent variables and cognitive demand as dependent variable. The results shows that betweenness ...
46 views

### Questions about adding polynomial features to a dataset for linear regression

Apologies if this belongs to Data Science instead of here (I can move the question) but this seems related to the math aspect more than ML. In our course we just ...
28 views

### Power analysis for orthogonal polynomials

Use GPower for power analysis for cubic estimator in orthogonal polynomial regression? I would like to determine the sample size I need in order to find a significant cubic estimator in an orthogonal ...
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### Probability distribution derivation given histogram of outputs

I'm not too versed in statistics, but I am currently dealing with a problem that pertains to probability. If any assumptions are off on my part, please correct me. I have a 2D polynomial function of ...
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### What can this polynomial regression tell me about the distribution of my error values?

I'm working with a list of errors in some process that can be expressed as small percentages. Since they're errors we hope they're small overall and expect them to be approximately normally ...
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### Why my Polynomial model has this spike?

How can I explain the spike in my Poly model after using the polynomial 3rd degree? My dataset consist of the X variables external facctores (x1,x2...xk) and Y which is a target variable. For a ...
1 vote
114 views

### How to Choose Polynomial Degree for Regression Model when Error Keeps Reducing As Degree Increase

I have a relatively small dataset with less than 100 samples, with one predictor and one outcome variable, both numerical. I generated models using lm and glm functions. For linear and polynomial (2 ...
37 views

### How to learn from a dataset of weighted polynomials

I have a dataset of weighted polynomials, i.e. each data point is a polynomial (of variable size/degree) together with a weight vector (of fixed size). Each data point has an integer label that ranges ...
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### Use of polynomial regression when I can identify more curves

Hello I am modeling a regression for my school project and one of the question I got from my professor was, how would I model this with polynomial regression. I have quite good random forest and knn ...
1 vote
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### Fitting a set of points to a distribution by adding up to three degrees of freedom with Python [closed]

I have a set of points whose shape is as below: Its set of x and y points is as follows: x=[0.14741,0.180288,0.195,0.245342,0.25614,0.289377,0.315789,0.357143,0.431034,1.785714,2,2.323529,2.586207,3,...
140 views

### Mean centering polynomial regression model

I have had to include a squared term in my regression model due to observed non-linearity in the LOWESS plot. In my reading to understand how to interpret the coefficients on the linear and squared ...
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1 vote
170 views

### Why is my polynomial regression with gradient descent not overfitting?

I wanted to implement linear regression with gradient descent from scratch and demonstrate how you can overfit when using too many polynomials. Unfortunately my model does not really overfit the data. ...
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### interpreting polynomial regression output when the regressors are orthogonal (vs. raw)

I want to show an inverted U-shape relationship between two variables: "minutes spent in a room A" and "trustworthiness in others". The hypothesis is that those who have low and ...
205 views

### Is there such a thing as polynomial multivariate panel regression?

I am to analyze a set of economic variables, taken from multiple countries, and recorded across time. This is certainly a panel dataset. If I'm not mistaken, the pooled OLS, fixed and random effects ...
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### How to recover the formula of the polynomial regression model?

I am trying to recover the formula of my regression model. I build the polynomial regression model using ...
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1 vote
27 views

### Are polynomial models unreliable at data extremes? [duplicate]

I have fitted a polynomial regression (4 degree model) to describe a non-linear relationship between my two variables. My question is why does this model begin to decrease towards the right hand side ...
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1 vote
146 views

### Select polynomial order for continuous variables in mixed model step-wise backward selection

I am working on some data that I would like to analyze through a generalized linear mixed model regression and a stepwise backward selection of variables directly on that model. I use the GLMERSelect ...
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### k=Fold Cross Validation Issues

I am trying to do a k=fold cross-validation on a polynomial regression. Unfortunately, I am getting an MSE that is vastly different from the MSE I would get if I were to just manually change the ...
60 views

### If first degree polynomial models are linear models, why do results of linear model differ from that of poly(x,1)? [duplicate]

As the title reads, the results from the linear and first degree polynomial model are different and I am not sure why. Any ideas why this might be? ...
252 views

### How do I perform error propagation of a polynomial function?

I'm trying to perform error propagation for some photometry code I'm writing, but I'm having some trouble with it! I have a value $x$ that I draw from a distribution with standard deviation $\sigma_x$,...
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### Does it make sense to use neural network in place of polynomial regression to fit 1 dimensional functions when only 1 feature is available?

As title says I would like to understand why there are so many tutorials and notebooks showing how to fit 1 dimensional functions with neural networks instead of polynomial regression. What are the ...
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1 vote
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### Polynomial regression has good Mean Squared Error but poor prediction on unseen data [closed]

In a dataset, the unseen target value is 2500000000. In a polynomial regression with degrees from 1 through 7, I have the following results: ...
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1 vote
47 views

### Determining whether fit parameter is necessary or not

I have a set of data parameterized by a single variable which is nearly perfectly linear, and I am trying to quantitatively determine with what confidence we can say a theoretical quadratic term is ...
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1 vote
70 views

### Quadratic regression with orthogonal polynomials vs. raw polynomials with QR decomposition

I'm using rstanarm to estimate random slopes for second-order polynomial coefficients. My model has the basic form: ...
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### Is this model significant? [duplicate]

I fitted a quadratic model on my data and got the following output: The Pr (>|t|) values were not significant (p<0.05) but the overall p-value of the model was. Is my model significant or not?
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### Polynomial Regression sensible in case with 6 cross-sectional points of experience?

I have a dataset of 300 cases of police students, spread over 6 semesters. They all filled out a survey at the same time (cross section), thus their experience is interval scaled since semester 1 ...
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### Inclusion of polynomial term in multiple linear regression

I want to predict risk perceptions with conspiracy beliefs and political orientation. Theoretically, I do not assume that political orientation is quadratically related to risk perceptions. My data ...
249 views

### Using GLM with poly() function to look if there is an optimum

I am looking for an optimum in weight for my research. I used: glm(formula = PCRresult ~ poly(Weight, 2), family = "binomial", data = dataset) In ...
1 vote
410 views

### How to interpret coefficients in polynomial linear regression?

The equation below stands for multiple linear regression model. $$Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots+ \beta_n X_n + \epsilon$$ The regression coefficients ($\beta$) are interpreted as ...
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### Interpreting Results of Logistic Regression when both x, y variables are nominal

I've been trying to analyze the result from my experiment. But since I'm new to the field of statistics, I'm struggling in every step, including the interpretation of results. I have 4 groups of ...
380 views

### Proof that a necessary condition for characteristic roots to lie inside unit circle is $\sum\limits_{i=1}^{n} a_{1} < 1$

I have been trying to show that given $$P_{n}(\alpha) = \alpha^{n} - a_{1}\alpha_{n-1} - a_{2}\alpha^{n-2}... - a_{n} = 0,$$ the $\alpha$'s that solve this equation (real-valued or complex) lie in the ...
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### R poly what family of polynomials? [duplicate]

The R poly function documentation says that it gives orthogonal polynomials, but it's not clear what orthogonal polynomials it gives. Are they Legendre? Are they ...
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### Help Understanding Polynomial/Least Squares Regression

I have a dataset of 2 variables (called x with shape n x 2 values of x1 and x2) and 1 output (called y). I am having trouble understanding how to calculate predicted output values from the polynomial ...
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