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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12 views

Non linear regression using R [on hold]

I am working on a prediction problem for continuous data. I have some data which I want to fit in the equations. It's non-linear in nature. Can anyone suggest me good non-linear regression algorithms ...
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0answers
6 views

JAGS equivalent to R's I() (Inhibit Interpretation of Objects) function?

I'm wondering if anyone has come across the JAGS/BUGS equivalent to R's I() function. I am interested in using this in a polynomial logistic regression, i.e.: mod1 <- glm(Employment ~ Density + ...
2
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1answer
32 views

Differing significance of linear and quadratic terms

I'm surprised this question has yet to be asked; hopefully it is an embarrassingly simple one. I am fitting a negative binomial regression with 12 total covariates (6 linear variables and 6 ...
1
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0answers
20 views

Relationship between Coefficients of Orthogonal Polynomial and Normal regression

So this is more a question to help me understand what is going on rather than application: So in normal regression we have $$ \mathbf{Y=X} \mathbf{\beta} + \varepsilon $$ Now the part that really ...
3
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1answer
85 views

Multicollinearity in polynomial regression

How to deal with multicollinearity in polynomial regression? Suppose I have $x$, $x^2$ and $x^3$ as independent variables in my regression equation. How can I calculate and remove multicollinearity ...
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1answer
80 views

Fit data to a bivariate function

I want to fit my (x,y,z) data points to a function. You can see the data on Fig.1. The data is symmetric along the main diagonal. To understand my data I have studied (y,z) curves at different ...
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0answers
78 views

Is this polynomial correct?

Disclaimer: I have no knowledge of stats. I fitted a polynomial to data points. I expected it to look like an exponential decreasing curve, but this seems to dip below zero, as well as the histogram ...
0
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0answers
29 views

backward shift operator as a sum (heuristic solusion)

I am interested in converting $(1-L)^n$ to a sum, where $L$ is backward shift operator. Let give you an example, \begin{align} \triangle^1 &=X_{i+1}-X_{i}\\ \triangle^2 & ...
5
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2answers
155 views

What is a reasonable noninformative prior for quadratic and cubic coefficients in Bayesian polynomial regression?

Say we have a Bayesian polynomial regression like the following. $$y_i \sim N(\mu_i, \sigma^2)$$ $$\mu_i = \beta_0 + \beta_1 x_i + \beta_2 x_i^2 + \beta_3 x_i^3 $$ where $x_i$ is some mean centred ...
1
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1answer
38 views

Regression against polynomials and log-linear predictors

I have a regression problem where one of the predictors has a very good fit as $Y \sim poly(X_1, 2)$. However, $Y$ is clearly log-linear against my second predictor $X_2$, so $ln(Y) \sim ln(X_2)$. ...
2
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1answer
55 views

Stability of univariate fractional polynomial models

I can't decide what is the best way to assess the stability of a higher order fractional polynomial model. To use an example I have been working on, I am analyzing a dataset with panel data selected ...
1
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1answer
35 views

Sign changes when I cube a variable in a linear model

In my linear model I have the variable of interest $x$, and a whole bunch of covariates that I condition on. The coefficient is significant and positive. I have reason to believe that the connection ...
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0answers
25 views

Comparing difference between two polynomial regression models in R [duplicate]

I've been having some trouble in attempting to compare sets of data. I can't seem to analyse whether two models describe the same set of data, or if they describe different sets. Here is my a portion ...
1
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0answers
48 views

How to perform a regression with orthogonal polynomials (such as laguerre) in R? [closed]

Using R software, I'm trying to perform a polynomial regression on E(Y|X1, X2, X3). In fact, E(Y|X1, X2, X3)must ne equal to a linear combination of polynomial with orthogonal basis (such as Laguerre ...
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0answers
76 views

Significant turning points in fractional polynomials

When using fractional polynomial models it has been suggested to use the first derivative of the polynomial function to identify significant periods of change and the second derivative to identify ...
2
votes
1answer
119 views

Local polynomial regression: Why does the variance increase monotonically in the degree?

How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)? This question has ...
0
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0answers
29 views

Calculating Polynomial Regression Confidence Bands

I have $N$ samples with known standard deviation: $(x_i, y_i \pm \sigma_i)$. I need to use order-$p$ least-squares polynomial regression to create confidence bands for $\hat y(x)$. I know R can do ...
0
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0answers
44 views

How to prove consistency of a non constant partial effect

Suppose a data generating process behaves according to the following hypotheses, where for simplicity $x$ is a scalar random variable that enters into the model linearly and through a quadratic term: ...
2
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1answer
140 views

Using B-splines within a linear mixed-effects model in R

I am using linear mixed-effect model (run with the lme() function in the nlme package in R) that has one fixed effect, one ...
0
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0answers
37 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 ...
6
votes
4answers
498 views

What are the formulas for exponential, logarithmic, and polynomial trendlines?

In creating linear trendline, I used the following formulas: $$y=mx+b$$ $$m = \frac{n\sum(xy)-\sum x \sum y}{n\sum x^2 - (\sum x)^2}$$ $$b = \frac{\sum y- m \sum x}{n}$$ and this for the R-squared: ...
4
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1answer
43 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
33 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 ...
1
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1answer
157 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
73 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
54 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 ...
1
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1answer
101 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 ...
0
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0answers
42 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: ...
0
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1answer
66 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
145 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
votes
2answers
105 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
votes
1answer
64 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. ...
0
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0answers
28 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
51 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
votes
1answer
32 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 ...
0
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0answers
36 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
23 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
46 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?
6
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3answers
256 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
vote
1answer
111 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
36 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
545 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
votes
0answers
26 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
38 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 ...
9
votes
3answers
267 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
383 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
votes
1answer
146 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
95 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
65 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 + ...
1
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2answers
196 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 ...