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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10 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
30 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?
5
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3answers
124 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 ...
1
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1answer
45 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 ...
0
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0answers
26 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 ...
4
votes
2answers
272 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
20 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
27 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 ...
8
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3answers
212 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
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3answers
328 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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0answers
15 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 ...
0
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1answer
53 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
80 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 ...
0
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1answer
37 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 + ...
0
votes
0answers
50 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 ...
1
vote
2answers
86 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 ...
4
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3answers
549 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
247 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
29 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 ...
0
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0answers
68 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 ...
0
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0answers
69 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
94 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

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
50 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 ...
1
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1answer
159 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
vote
1answer
76 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
185 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
151 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
81 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: ...
0
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0answers
394 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 ...
0
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0answers
88 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
77 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
88 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, ...
3
votes
2answers
876 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
votes
0answers
60 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
votes
0answers
76 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 ...
4
votes
2answers
10k 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
votes
0answers
111 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 ...
3
votes
1answer
302 views

How would you report (in publication) the results of a linear model fit using the poly function in R?

@John recently pointed out to me that R's poly function produces less correlated values (more orthogonal) to fit polynomial predictors, i.e. the transformed ...
6
votes
3answers
931 views

Perform linear regression, but force solution to go through some particular data points

I know how to perform a linear regression on a set of points. That is, I know how to fit a polynomial of my choice, to a given data set, (in the LSE sense). However, what I do not know, is how to ...
1
vote
1answer
64 views

nearest neighbors degrees of freedom

For polynomial fitting with a polynomial of degree $n$, we have $n$ degrees of freedom. Is there a similar concept for $k$ nearest neighbors? Is there any way to compare the degrees in general? I come ...
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0answers
237 views

Model reduction - Backward elimination

The rule I use for reducing covariates (trimming) is as following: Look at the highest order interaction. If that is not significant, drop it. If it is significant, stop. If drop the highest order ...
2
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1answer
91 views

Sample point locations and multiple linear regression

I have a question on multiple polynomial regression and the absolute minimum amount of points in the different terms. The minimum amount of points required for a second order polynomial would (in one ...
2
votes
4answers
571 views

comparing predictive model with hold out set

In Rapid Miner, I created a predictive model (SVM) with Kernel type = polynomial, c= 10, and obtained 80.77% accuracy using cross validation. When compared to hold out set my accuracy on the test ...
2
votes
1answer
451 views

Calculating Adjusted $R^2$ in Polynomial Linear Regression with Single Variable

When calculating Adjusted $R^2$ the formula is $1-(1-R^2)\frac{n-1}{n-k-1}$ with $k$ being how many predictors you have. If I am using a model with a single variable but that variable has been put ...
9
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1answer
2k views

Can I interpret the inclusion of a quadratic term in logistic regression as indicating a turning point?

In a Logistic Regression with linear and quadratic terms only, if I have a linear coefficient $\beta_1$ and quadratic coefficient $\beta_2$, can I say that that there is turning point of the ...
3
votes
1answer
504 views

Two negative beta's in a curvilinear regression when mean centered or using standardized values

The problem I encounter is the following: Imagine a (perfect) inverted U-shaped relation between an independent variable and a dependent variable. When you look at the curve estimation there is ...
3
votes
2answers
532 views

Improvement of regression model

I am just learning R. I have developed a regression model with six predictor variables. While developing it, I found the relationships are not very linear. So, maybe because of this the predictions of ...