# Tagged Questions

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### 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 ...
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### Polynomial in linear regression

I am new to Regression and R. I know that polynomial functions are used when a regression model does not fit data (underfitting), but I want to know which degree of polynomial should be used? I also ...
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### 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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### 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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### Dynamic consistency and multilevel models using lmer

I've been using nlme and more recently lmer to fit multi-level models of time course data using orthogonal polynomials. My ...
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### Recovering raw coefficients and variances from orthogonal polynomial regression

It seems that if I have a regression model such as $y_i \sim \beta_0 + \beta_1 x_i+\beta_2 x_i^2 +\beta_3 x_i^3$ I can either fit a raw polynomial and get unreliable results or fit an orthogonal ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### lm to lmer function tweaking

I have stolen and modified a snippet of code found off the internet from (http://www.r-bloggers.com/aic-bic-vs-crossvalidation/) which graphically depicts AIC and BIC values for different polynomial ...
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### Orthogonal contrast with an ordinal variable in GAM

I am fitting a set of continuous and factor variables into a GAM. The factors are ordinal: they are levels of abundance of specific macroinvertebrates set as "none" (0% cover), "low" (>0-10% cover) ...