# Tagged Questions

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### Find polynomial in 3 input variables that predicts 2-dimensional output variable in Matlab [migrated]

I have a system where three input variables (x1, x2, x3) predict two output variables (y1, y2). I would like to find a polynomial function f such that f(x1, x2, x3) = (y1, y2) + error. where the ...
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### Estimation of a power function in regression $y = ax^k$

I'm performing a case of polynomial regression. I use a power $k$ for the regressors (e.g. marketing spend), which helps me determine the nature of the response curve. I also need to estimate the ...
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### Python creating a polynomial model with two input variables

I have data for two input variables x_1 and x_2 and one output variable y. The two input variables seem to have a nonlinear relationship with y. Here are the plots So I am trying to fit a ...
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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 ...
271 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 ...
4k 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 ...
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### 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 ...
455 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 ...
355 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 ...
386 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 ...
329 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 ...
277 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 ...
376 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 ...
376 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 ...
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### 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 ...