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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1answer
51 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
13 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
35 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
46 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. ...
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1answer
47 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 ...
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1answer
44 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
20 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
31 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
27 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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27 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?
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0answers
18 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 ...
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1answer
35 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
178 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
68 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
31 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
346 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
21 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 ...
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1answer
29 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
230 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 ...
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3answers
349 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 ...
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0answers
16 views

Polynomials and NSA

I'm looking for some applications of criteria of irreducibility of integer polynomials inside and outside mathematics. I was reading the CV of Filaseta, a great researcher in this area, and he has ...
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1answer
72 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 ...
1
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1answer
85 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
47 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
62 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
110 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 ...
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3answers
900 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 ...
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1answer
372 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 ...
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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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0answers
108 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
83 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
109 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
68 views

Polynomial regression analysis with response surface analysis for pre and post cortisol data and EI scores

I have done a study looking at the role of Emotional Intelligence in helping an individual regulate stress when they are abused by their boss. I took salivary cortisol samples before and after an ...
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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
19 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
168 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
81 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
212 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
180 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
88 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
2k 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
494 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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93 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
88 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
98 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, ...
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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 ...
2
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0answers
61 views

Can the OLS residual variance suggest a polynomial relationship?

I am trying to figure out whether from the following graph of the OLS residuals that the linear relationship does not hold, and that probably a cubic relationship would do better? Since both in the ...
2
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0answers
78 views

Unit root test for ARIMA models

I have a slight confusion regarding seasonal models and which polynomial to use for conducting unit root tests. Given a model: $\phi(B)\Phi(B^s)\Delta^d\Delta^D_S X_t = \theta(B)\Theta(B^s)\epsilon ...
7
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2answers
12k views

What happens when I include a squared variable in my regression?

I start with my OLS regression: $$ y = \beta _0 + \beta_1x_1+\beta_2 D + \varepsilon $$ where D is a dummy variable, the estimates become different from zero with a low p-value. I then preform a ...
2
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0answers
119 views

Orthogonality of Hermite Polynomials

As we know probabilistic Hermite polynomials are orthogonal with respect to the weight function $\frac{1}{\sqrt{2 \pi}} e^{-x^2/2}$ (density of standard normal). I have a distribution which is a ...