# Questions tagged [polynomial]

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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### Books on Polynomial Regression

I have read some books on statistics, and it covers most of the regression algorithm, but does not cover up much on polynomial regression. Any suggestions on books covering up this topic, specifically ...
5k views

### R polynomial expansion error on “unique points” and degree

Why I am getting errors in R for "'degree' must be less than number of unique points" in this case? ...
661 views

### Orthogonal polynomials for regression

Is it possible to define orthogonal polynomials on the interval $[0, +\infty[$ ? Maybe using the Gram-Schmidt process from the monomial basis $(1, x, x^2, ...)$? My problem is that I have some data ...
696 views

### Rank of a matrix in Polynomial regression model?

We know, that by the assumption the rank of matrix $X$ in linear model is $k$, where $k$ is nummber of columns. What about polynomial regression model? What is the rank of matrix $X$ in this model?...
2k views

### R2 cross validation metric vs linear regression R2

I've been using sklearn for a project I'm working on. I'm following this example for analyzing my data. I believe I have an overfitting problem, but before I try to address it I want to make sure I'm ...
182 views

### What's the justification for normalizing inputs when solving using closed form?

In Machine Learning I understand that feature scaling or mean-normalizing your input is useful when trying to learn a model using gradient descent. It's useful in the sense that it speeds up training ...
3k views

### Why are there large coefficents for higher-order polynomial

In Bishop's book on machine learning, it discusses the problem of curve-fitting a polynomial function to a set of data points. Let M be the order of the polynomial fitted. It states as that We ...
223 views

### R: Fit sinusoidal curve to timeseries, and interpolate at desired times

I have ocean tide data with just high and low tides. I need to fit an appropriate curve (sinusoidal presumably, maybe just polynomial) to this, and then extract values interpolated at specific times. ...
987 views

### When to report quadratic versus linear relationships

I seem to remember from my graduate statistics course that if higher order variables (i.e., X^2, X^3, etc) are significant in a polynomial regression analysis such as our quadratic regression, then ...
252 views

### How can I fit a polynomial given some prior knowledge but fewer observations than coefficients?

I want to fit a second degree polynomial to data from a fractional factorial design in five dimensions. Because of the cost of trials, I am initially only going to do eight runs. So I have fewer ...