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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19 views

Comparison of Non-Stationary Time Series Trends

I am trying to compare two readings of the same occurrences from two different sources, forming two time series. I would like to assign a metric to their similarity/dissimilarity, but the method I am ...
4
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1answer
23 views

Does a polynomial kernel with degree less than 1 satsify mercers condition

Consider the polynomial kernel: $$K(\boldsymbol{x}, \boldsymbol{x}') = (\boldsymbol{x}^{T} \boldsymbol{x}'+c)^{d}$$ This kernel satisfies the mercers theorem/condition. Since I never saw any ...
2
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0answers
24 views

How to determine significance of polynomial?

I'm running a model where both a 2nd or 3rd order polynomial would seem to fit the data. I'm trying to decide which one to use. In the quadratic model (panel fixed effects) the first and second order ...
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1answer
122 views

Fractional polynomials vs GAMs

I have been analyzing panel data for a while now using different methods (Generalized Linear Models, fractional polynomials and GAMs). If we just ignore GMMs for now, I have come to find that ...
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0answers
47 views

Polynomial transform of a Gaussian Random Variable

I have been trying to find how the PDF of a polynomial transform of a Gaussian Random Variable could be found. Eg: If \begin{equation} \ X\sim N(\mu,\sigma^2) \end{equation} Then what would be the ...
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1answer
32 views

Reduce the polynomial terms in logistic regression (glm)

I've three categorical variables A, B and C with 5 levels each. The model I'm trying to fit is glm(Y~A+B+C, family=binomial()) How can I remove the higher order ...
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1answer
60 views

What is the value of “X” in a regression equation when dealing with a time series?

I am using excel to add a polynomial trend line to a chart. The chart and the formula of the trend line are shown below. I want to add lines indicating different confidence intervals so I need to find ...
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0answers
24 views

Should I standardize or rescale with polynomial regression as alternative to difference scores?

I am working with a model that uses polynomial regression combined with response surface modelling as an alternative to difference scores in regression: ...
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1answer
44 views

Polynomial regression P value is getting altered

I am running following data and code for analyzing non-linear regression and to get simplest equation of curve that fits the data: ...
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0answers
70 views

How to determine if GLM quadratic term should be set up orthogonal or non-orthogonal

I am setting up a GLM in R where I have only one predictor variable and its quadratic form. I understand that in R I have 2 options. ...
2
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1answer
57 views

Maximum Degree of Polynomial Regression

If we have 100 data points and want to perform polynomial regression, the maximum degree of our polynomial is n-1, where n is the number of data points. In this case, the maximum degree would be 99. I ...
3
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1answer
51 views

Changing polynomial degree leads to changing p-values in OLS regression

I have a question about interpreting coefficient $p$-values when fitting a polynomial function with ordinary least squares. When I sequentially fit a linear, then quadratic, then cubic etc. ...
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0answers
22 views

Sample size for validating a prediction model

Dear friends: In an earlier pilot study a third- degree polynomial model was built, X = time (days) Y = Moisture loss. I need to validate this model in a larger study with more samples. ...
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1answer
36 views

Rank deficiency in polynomial trend analysis

I am currently trying to fit a model for some reaction time data from an experiment with four consecutive blocks of the same task. I am interested whether there is something like an effect of practice ...
2
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1answer
28 views

What kind of functions can have non whole degrees?

Thanks for the help in advance. I am reading a technical report on a regression algorithm that reports a pair of functions as having a total degree of freedom of 5.4. I believe that both of these ...
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0answers
31 views

polynomial regression model

I have 8 parameters with 3 levels and the number of tests required to study this case is 27. Can I generate polynomial regression model to describe interaction of these parameters?
2
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0answers
21 views

Polynomial Data Fitting for Two Unknown Equation

I have a kind of data and want to find the equation(poly coeff) of given data. For example equation for given sample data is simple a^2*b+10 ...
2
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1answer
39 views

Polynomial regression rules

With OLS regression the errors must be normally distributed and be homoscedastic. Does these rules apply to polynomial regression as well?
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3answers
200 views

How to interpret coefficients of $x$ and $x^2$ in same regression

If I have the below functional form for an OLS regression, how do I interpret the $x$ and $x^2$? I cannot interpret them separately, correct? Do I interpret them as a summation of the two ...
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1answer
83 views

Compute mode of a quadratic regression with confidence intervals

I have a quadratic regression y against x and I'm interested in the value x where y is the maximum (ymax->x). I can compute x(ymax) but I'm also interested in the standard error or confidence ...
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0answers
34 views

How to find out some particular distribution given the grouped data and a polynomial fitted to the data

I have to analyse a set of grouped data.The data is divided into groups by some categories for example: BP(<=60), BP((60,80]); Pulse(<75), Pulse((75,90]) & Pulse(>90) etc having many more ...
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2answers
385 views

Is there ever a reason not to use orthogonal polynomials when fitting regressions?

In general, I'm wondering if there it is ever better not to use orthogonal polynomials when fitting a regression with higher order variables. In particular, I'm wondering with the use of R: If ...
2
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0answers
22 views

Polynomial model with unpaired data

I'm trying to model data as a 2nd degree polynomial, but the data is unpaired and each data point of average values has a standard error for each axis. My data: A time series in minutes (time ...
1
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1answer
31 views

The impact of rescaling a predictor on the standard error of the corresponding coefficent

I am trying to form a polynomial regression model using SVD linear model. As the predictor at a large degree goes too large, say x6, I first scale it down if the mean of x6 is over a threshold and ...
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3answers
235 views

How to include $x$ and $x^2$ into regression, and whether to center them?

I want to include the term $x$ and its square $x^2$ (predictor variables) into a regression because I assume that low values of $x$ have a positive effect on the dependent variable and high values ...
4
votes
3answers
365 views

Any algorithms better than polynomial regression

I am trying to fit a baseline through my data, and I am not getting close enough with polynomial regression. I used gradient descent to set the parameters. Are there any other ways or algorithms that ...
0
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1answer
89 views

Denormalizing Data

I am applying Polynomial Regression to my data, however the parameters theta were always =0, i noticed that my y data or output is too large in the order of 100000 so i normalized y, i got very good ...
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1answer
86 views

How to determine exact point of tangency?

I have fitted my stress-strain data with $y=ax^3+bx^2+cx+d$ and also added tangent lines as shown in figure below. I am interested to see the deviation of the fit from the linearity. I am not aware of ...
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1answer
52 views

Using inverse of cube In linear model

What's the formula for a equation that can produce the continuum from the red to green lines in this graph below? I can easily get anywhere from the green line to the blue with $$y = B_0 + B_1x + ...
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0answers
67 views

How to smooth time-series NDVI data using polynomial regression

I have a time-series NDVI image. The image has 26 bands. 26 bands mean that images taken in 8-day time interval and counted in Julian days (97 to 297). For example; first band of the image is NDVI ...
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2answers
128 views

Best practices for extrapolating data

I have a set of variables that parameterize a logistic equation bacterial growth model. The parameters change based on temperature (e.g., growth speeds up at higher temperatures) and so it is ...
7
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3answers
1k views

Why is polynomial regression considered a special case of multiple linear regression?

If polynomial regression models nonlinear relationships, how can it be considered a special case of multiple linear regression? Wikipedia notes that "Although polynomial regression fits a nonlinear ...
3
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1answer
443 views

Polynomial term in logistic regression

I've made a logistic regression model that includes a polynomial term to degree 2. I'm aware that logistic regression models the response variable as a non-linear function of the predictors. Does it ...
0
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0answers
35 views

Subjects:condition interaction random effect in a growth model

I'm investigating the effect of 'Condition' (3 levels: Quiet, Intelligible, Unintelligible) on pupil response over time (intercept, linear, cubic, quadratic, quartic and quintic terms). When I use ...
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119 views

Growth curve analysis on orthogonal polynomial terms

I am conducting a study which is looking at the effect of 'Condition' (Quiet, Intelligible, Unintelligible) on the pupil(eye) response over time. Upon visual inspection of my data plots, pupil ...
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0answers
95 views

Feed-forward GMDH-type Neural Network model in R

I wish to build Feed-forward GMDH-type Neural Network model in R. The most popular base function used in GMDH is the gradually complicated Kolmogorov-Gabor polynomial as explained in wikipedia. Any ...
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0answers
114 views

Is it possible to center orthogonal polynomials in multiple regression

I have a regression model that looks like the one below. $$ Y = \beta_0 + \beta_1T + \beta_2T^2 + \beta_3T^3 + \beta_4D + \beta_5D*T + \beta_6D*T^2 + \beta_7D*T^3 $$ Where ...
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0answers
55 views

Optimal Rotation Before Curve Fitting

I am fitting a 1-dimensional polynomial to a set of data points $\{(x_1,y_1,z_1),...,(x_N,y_N,z_N)\} \subset \mathbb{R}^3$ using least squares regression. My first instinct was to choose $x$ as an ...
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0answers
21 views

Number of trials needed to increment a counter variable

Truthfully I'm not even sure what the proper name for this sort of trial is, so I'll just describe the whole setup. Suppose I have an integer variable n, which starts at zero and gets incremented ...
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1answer
174 views

Overcoming small dataset anomalies in genetic algorithm

So I am currently making my 6th version of a model designed to predict the likelihood of of a particular medical condition based on a multifactorial genetic markers and I really would appreciate some ...
1
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1answer
84 views

How to algorithmically determine the best order of fit?

I am doing a least squares polynomial interpolation for 10,000 data sets that look mostly like one period of a sine curve, but whose values are not evenly spaced in the time domain, and can sometimes ...
4
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0answers
230 views

Optimal orthogonal polynomial chaos basis functions for log-normally distributed random variables

I hope this is the appropriate venue for this type of question. If not, please feel free to migrate! :) I'm trying to solve a stochastic partial differential equation of the form ...
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1answer
188 views

Estimation of a power function in regression $y = ax^k$

I'm performing a case of polynomial regression. I use a power $k$ for the regressors (e.g. marketing spend), which helps me determine the nature of the response curve. I also need to estimate the ...
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0answers
94 views

Where does the square root for a polynomial kernel mapping function come from?

I'm trying to understand how polynomial kernel functions work, in my textbook it shows an example with a degree of 2, with an input dimension of 2: $K(\vec{x}, \vec{y})$ = $(1 + x_1y_1 + x_2y_2)^2$ ...
3
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2answers
3k views

Getting a second-order polynomial trend line from a set of data

Alright, so I have about a thousand datapoints that I'm plotting on a chart (scatter plot). Here's a few of the records: ...
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0answers
573 views

Python creating a polynomial model with two input variables

I have data for two input variables x_1 and x_2 and one output variable y. The two input variables seem to have a nonlinear relationship with y. Here are the plots So I am trying to fit a ...
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0answers
96 views

cross-validation and standardization

In this thread @whuber gave detailed answer about using training data statistics for standardizing cv dataset. My question is how to standardize hold-out dataset in n-fold cross-validation if some ...
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0answers
94 views

How to select the degree of polynomial multiple regression?

I have around 50 dependent quantities (regressor variables). I want to find the best relation between the response variable data and regressor variable data. I tried multiple linear regression with ...
4
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0answers
103 views

Computation of polynomial contrast variables

Please give me idea how to efficiently recode a categorical variable (factor) into the set of orthogonal polynomial contrast variables. For many types of contrast variables (e.g. deviation, simple, ...
5
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3answers
1k views

Polynomial regression using scikit-learn

I am trying to use scikit-learn for polynomial regression. From what I read polynomial regression is a special case of linear regression. I was hopping that maybe one of scikit's generalized linear ...