A mathematical expression w/ >1 term containing the same variable (eg, x & x^2). Polynomials are commonly used to model curvilinear relationships.

learn more… | top users | synonyms

0
votes
0answers
67 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
votes
0answers
19 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
votes
2answers
136 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
vote
1answer
36 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
votes
1answer
39 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
vote
1answer
24 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 ...
0
votes
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
vote
0answers
25 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 ...
1
vote
0answers
54 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
104 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
votes
0answers
20 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
votes
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
votes
1answer
70 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
votes
0answers
31 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
334 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
votes
1answer
31 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
votes
0answers
28 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
vote
1answer
143 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 ...
1
vote
0answers
63 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 ...
-2
votes
1answer
48 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
vote
1answer
74 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
votes
0answers
33 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
votes
1answer
60 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: ...
1
vote
0answers
113 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
1answer
71 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
55 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
votes
0answers
25 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. ...
1
vote
1answer
45 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
29 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
votes
0answers
34 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
votes
0answers
21 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
votes
1answer
43 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
votes
3answers
229 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
99 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
votes
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
460 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
24 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
vote
1answer
35 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
249 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
375 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
118 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
vote
1answer
93 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
votes
1answer
56 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
75 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
155 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 ...
9
votes
3answers
1k 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
votes
1answer
587 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 ...
1
vote
0answers
125 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 ...
1
vote
0answers
59 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 ...
1
vote
0answers
28 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 ...