# How to OLS several lines at once?

• phrozenfearz
In summary, the speaker is seeking guidance on how to fit a regression to multiple sets of data that all share the same ideal data set. They are struggling to find resources on multiple regression and are looking for a method that can account for the variation in pressure in their experimental data. Their ultimate goal is to create a curve that represents the relationship between [x] and [y] across the entire pressure range of their experiment.
phrozenfearz
Hello PhysicsForums.com!

I've got several sets of data that are all intended to represent the same ideal data set. I need to fit a regression to said sets of data - but have no idea of how to go about it.

All multiple-regression literature I can find reads to the tune of: given y=a*f(x1)+b*f(x2), but I don't have multiple dependence on x. I just have 9 sets of equations that all look like:
Point 1...
y1=f(x1)
y2=f(x2)
y3=f(x3)
Point 2...
y1=f(x1)
y2=f(x2)
y3=f(x3)

If somebody could point me in the right direction, I would be very appreciative!

Thanks!

Are you talking about Vector Autoregressive Model?
yt=a*y_t-1+b*x_t+...et
xt=c*x_t-1+d*y_t+...,ut

I don't think so... but please elaborate more on the method.

In return, I'll elaborate more on what I have and what I need:

I have several sets of [x] and [y] data series, taken by experiment, on separate occasions. The experimental setup, in terms of the two variables I need to fit a curve to, only varies in pressure. The variation comes in a slight translation along the x-axis.

My goal is to fit a curve to ALL of these data sets to act as an approximate representation of [y] in terms of [x] across the pressure range from the experiment.

Thanks!

## 1. Can I perform OLS on multiple lines of data simultaneously?

Yes, it is possible to perform Ordinary Least Squares (OLS) on multiple lines of data simultaneously. This can be done using multivariate regression, where the dependent variable is a combination of multiple independent variables.

## 2. What is the benefit of OLS on multiple lines compared to one at a time?

Performing OLS on multiple lines at once allows for a more comprehensive analysis of the relationships between the dependent variable and multiple independent variables. It also allows for the identification of any interactions or correlations between the independent variables.

## 3. How do I interpret the results of OLS on multiple lines?

The results of OLS on multiple lines can be interpreted similarly to OLS on one line, with the addition of considering the relationships between the independent variables. This can be done by looking at the coefficients and their significance, as well as the overall fit of the model.

## 4. Is there a limit to the number of lines that can be used in OLS?

There is no specific limit to the number of lines that can be used in OLS. However, it is important to consider the sample size and the complexity of the model, as including too many lines can lead to overfitting and unreliable results.

## 5. What are some common mistakes to avoid when performing OLS on multiple lines?

Some common mistakes to avoid when performing OLS on multiple lines include not checking for multicollinearity between the independent variables, not considering the assumptions of OLS, and not properly interpreting the results. It is also important to ensure that the model is not overfit, and to use appropriate techniques for model selection and validation.

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