The polynomial tag has no wiki summary.
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40 views
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 ...
2
votes
1answer
42 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
40 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 ...
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0answers
39 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 ...
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0answers
15 views
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) ...
2
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2answers
549 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
66 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
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1answer
125 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 ...
5
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3answers
292 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
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0answers
26 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
98 views
SVM with svm and svmpath function
I am trying to compare the R functions svm (library: e1071) and svmpath (library svmpath).
...
0
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0answers
99 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
votes
1answer
68 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 ...
1
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4answers
226 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
244 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 ...
6
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1answer
512 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 ...
2
votes
1answer
270 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
246 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 ...
-1
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1answer
215 views
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 ...
2
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1answer
256 views
What is the role of a categorical predictor in polynomial regression?
I understand that there is a function in R called poly() that can generate orthogonal polynomials--useful for applying on input variables before running a ...
3
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0answers
271 views
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 ...
6
votes
1answer
356 views
Why do I get wildly different results for poly(raw=T) vs. poly()?
I want to model two different time variables, some of which are heavily collinear in my data (age + cohort = period). Doing this I ran into some trouble with lmer ...
1
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1answer
363 views
How to produce a polynomial trend line equation that takes three arrays as parameters?
Does anyone know of any programming code for producing a polynomial trend line equation that takes three arrays as parameters, ie X, Y and Weight?
Or even if you could explain in English how such a ...
18
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3answers
4k views
Does it make sense to add a quadratic term but not the linear term to a model?
I have a (mixed) model in which one of my predictors should a priori only be quadratically related to the predictor (due to the experimental manipulation). Hence, I would like to add only the ...
4
votes
1answer
83 views
Monomial distribution of $X^a \cdot Y^b$
What is the distribution of the following monomial?
$$X^a \cdot Y^b$$
where $X$ and $Y$ are normal random variables and $a$ and $b$ are natural numbers.
For example, when $X \sim N(0,1)$, $a=2$, and ...
1
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0answers
99 views
Determining polynomial model coefficients forcing slope = 1 and intercept =0
I have two observational variables, Cobs and R, both subject to measurement error. I believe that a model of the form Cmod = a0 + a1*R + a2*R^2 + a3*R^3 would be a reasonable representation of the ...
3
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1answer
554 views
Using Fractional Polynomials for Logistic Regression Modelling in R
I am learning logistic regression modeling using the book "Applied Logistic Regression" by Hosmer.
In chpaters, he suggested using Fractional Polynomials for fitting continuous variable which does ...
3
votes
3answers
265 views
Does the p-value in the incremental F-test determine how many trials I expect to get correct?
I've implemented an incremental F-test program that evaluates the fit of an unrestricted model $M_{UR}$ against the restricted model $M_R$ using the F statistic $\frac{SSE_{R} - ...
5
votes
2answers
261 views
Is there a fast algorithm to check for AR(p) stationarity?
It is well-known that an AR(p) process
$$
x_t=\sum_{i=1}^p \varrho_i x_{t-i} + \epsilon_t \,,
$$
is causal and stationary if and only if the roots of the polynomial
$$
\mathcal{P}(u) = 1 - ...
