Recent content by CopyOfA

This is a clever way of setting up the problem. I'll play around with this, and with any luck, this thread will be closed. Thanks again!

From what I can tell, the data ##\mathbf{y}_i## at each ##x_i## is not normally distributed. This is one reason that I'm hoping to find some other methods of regression beyond simply fitting through the means.

Simple linear regression would minimize the L2 norm, if the data were normally distributed (or I suspect, symmetric). As I mentioned, if the data ##\mathbf{y}_i## at each ##x_i## were normally distributed (or perhaps just symmetric), then simple linear regression on the mean would be absolutely...

Fair enough. What I'm trying to do is estimate a linear fit through all of my data. Fitting through the mean is appropriate for normally distributed data. That is, if we assume ##\mathbf{y}_i## (##i##th row of the matrix ##\mathbf{Y}##) is distributed ##~N(\mu_y(x_i),\sigma_y)##, then we can...

OK, but I'm not really even sure how to do this... Consider linear regression on two variables. $$\mathbf{y} = \begin{bmatrix} y_1 \\ y_2 \\ \vdots \\ y_n \end{bmatrix}= \mathbf{X}A = \begin{bmatrix} 1 & x_1\\1 & x_2\\ \vdots & \vdots \\ 1 & x_n\end{bmatrix} \begin{bmatrix} a \\ b...

I do have all the data. In what way should I use all the data? Is there some bootstrapping method or performing multiple regressions over randomly chosen data?

Yes, this is absolutely the case with my data. The time stamps are in order such that t1<t2<...<tn. Are there better ways of doing regression that simply regressing on the mean or median of the data at each time stamp? Is the mean or median preferred? How should I evaluate the fit? I'd prefer...

Unfortunately, I don't think I'm being clear, and admittedly my title does not convey the actual problem. My issue isn't on regressing with discrete variables per se, but with the combination of discrete independent variables and continuous dependent variables. Typically in regression one has a...

So just to be clear on the problem. Think of the independent variable as time and I have 27 time stamps. At each time stamp I have 50 data points for the dependent variable (i.e., at t=1, there are 50 data points that are continuous, same at t=2,...,27). This can be imagined as a sequential box...

Hey, I have a problem where I have a discrete independent variable (integers spanning 1 through 27) and a continuous dependent variable (50 data points for each independent variable). I am wondering about the best method of regression here. Should I just fit to the mean or median? Is there a way...

I've been attempting to model a simple electromagnetic coil using HFSS, and have so far been unsuccessful. I have no problems constructing the coil; this is a simple geometry problem. I have a wire of a known geometry with insulation surrounding the wire, then a construct a helical path and then...

Homework Statement We are given a wedge configuration with three sections. There are two conducting planes held at zero potential that make an angle of ##2\beta## with each other. They are connected by a portion of a conducting cylinder with radius ##a##. An infinite uniform line charge of...

This is a long post. Sorry... 1. Homework Statement We are given a spherical capacitor with an inner conductor of radius ##a## and outer conductor of radius ##c##. The space between the conductors is half filled (##a<r<b##) with a dielectric with permittivity...

Thanks for all the input everyone. I'll try my best to respond to everyone, if possible. Do you mean something like this (with the other end of the DUT terminated into a SMA cable in a similar fashion): My only experience with TDR has been with surface mount components that were arranged...

Right, I am not trying to do TDR for a small wire, as shown in the picture. In that case, it would be easier to simply inspect the wire visually :). I am trying to understand how to apply TDR to a single wire for other purposes like long electrical connections or coils. What do you mean by the...