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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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,...
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General Non-Uniform Berry-Essen
Let $f_n(x)$ by the probability distribution function of a continuous r.v. $X_n$. $X_n$ converges in distribution to $X$, i.e. $|P(X_n < x) - P(X < x)| \rightarrow 0$. On the top of that, $E[|...
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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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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 ...
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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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Learning a mapping function from one polynomial to another using a NN
I am interested in solving a problem that converts one set of polynomial coefficients (expressed as a vector of length N) to another set of coefficients (also a vector of length N) using a NN.
To give ...
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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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To nonparemetrically estimate the conditional mean of a binary outcome $E(D|x_1,x_2)$, can I use a logistic regression with flexible regressors?
Suppose $D$ is a binary outcome and $X_1$, $X_2$ are continuous regressors. I want to nonparametrically estiamte $E(D|X_1=x_1,X_2=x_2)$. I know that we could use local-constant or local linear ...
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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 ...
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polynomial orthogonal contrasts for ordinal independent variable with dummies for each level as well: collinearity problem?
If I have an ordered categorical variable as a predictor (independent) variable in a regression, can I also include the same variable as a nominal categorical variable, to prove that there is no ...
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Difference between polynomial data fitting and the regression model [closed]
What is the difference between polynomial data fitting and the regression model? The traditional regression used in LASSO is also just based on polynomial fitting, albeit linear. What is meant by &...
Ahmad Turani
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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?
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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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Multicollinearity in a polynomial regression
I am trying to understand what kind of problems multicollinearity in a polynomial regression cause. While doing so, I came across this set of lecture notes:
http://home.iitk.ac.in/~shalab/regression/...
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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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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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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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In quadratic regression, do I first need a significant linear effect before introducing the quadratic term? [duplicate]
I am working with a dataset that shows me an inverted U shape when I graph it. However, me and my colleague's are debating if I FIRST need a significant linear effect before doing a second regression ...
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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 ...
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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 ...
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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 ...
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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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How to do data imputation and normalization when using polynomial regression?
The question is about the practical use of polynomial regression.
Let's say there is a dataset with columns A, B, T where T is a dependent variable, A and B are independent variables. A and B contain ...
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Fit a polynomial model column of time series data
I'm asked to fit a polynomial model on the FTSE column from the EuStockMarkets dataset available in R. How is it possible to fit on just one column in this case? Is there another column of sorts in ...
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Log-Binomial Polynomial Terms Interpretation
I have a log binomial model of tested (yes/no) by number of years since 2011. The quadratic term is also significant. I am trying to find the probability of being tested at each year. I thought I ...
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Is it appropriate to fit a linear model to my data?
I have a bunch of outcome/exposure relationships I am trying to fit models to:
From these graphs, I am not sure if a simple lm is appropriate. Some of them look ...
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How can we explain the "bad reputation" of higher-order polynomials?
We all must have heard it by now - when we start learning about statistical models overfitting data, the first example we are often given is about "polynomial functions" (e.g., see the ...
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When adding polynomial features, the issue of multicollinearity doesn't hold. Why?
In the regression model, sometimes to capture the non-linear relationship between dependent and independent variables, we use polynomial features. But in regression, if the two or more features are ...
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Interpreting Quadratic Variables in Negative Binomial Regression
I want to include a quadratic term for age in my negative binomial model as past work has suggested it may be curvilinear. I know how to interpret a quadratic coefficient in OLS, but am unsure with ...
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Why are odd-degreed polynomial kernels slower than those with even degrees for SVM?
I have been using one-class support vector classifiers to extract features for multinomial classification. I noticed that fitting time is much longer when the degree of the polynomial kernel is odd. ...
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Backward elimination in multiple polynomial regression?
I'm working on multiple regression models (with R), and the use of polynomials can increase my adj r-squared. However, I'm a bit confused because if I add polynomials, the adj r-squared decreases, but ...
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