Regression Model for explained model(Details inside)

Question

I am kind of a newbie on machine learning and I would like to ask some questions based on a problem I have .

Let's say I have x y z as variable and I have values of these variables as time progresses like :

t0 = x0 y0 z0
t1 = x1 y1 z1
tn = xn yn zn

Now I want a model that when it's given 3 values of x , y , z I want a prediction of them like:

Input : x_test y_test z_test Output : x_prediction y_prediction z_prediction

These values are float numbers. What is the best model for this kind of problem? Thanks in advance for all the answers.

More details: Ok so let me give some more details about the problems so as to be more specific.

I have run certain benchmarks and taken values of performance counters from the cores of a system per interval.

The performance counters are the x , y , z in the above example.They are dependent to each other.Simple example is x = IPC , y = Cache misses , z = Energy at Core.

So I got this dataset of all these performance counters per interval .What I want to do is create a model that after learning from the training dataset , it will be given a certain state of the core ( the performance counters) and predict the performance counters that the core will have in the next interval.

Answer 1

AFAIK if you want to predict the value of one variable, you need to have one or more variables as predictors; i.e.: you assume the behaviour of one variable can be explained by the behaviour of other variables. In your case you have three independent variables whose value you want to predict, and since you don't mention any other variables, I assume that each variable depends on the others. In that case you could fit three models (for instance, regression models), each of which would predict the value of one variable, based on the others. As an example, to predict x:

x_prediction=int+cy*y_test+cz*z_test

, where int is the intercept and cy, cz, the coefficients of the linear regression. Likewise, in order to predict y and z:

y_prediction=int+cx*x_test+cx*z_test
z_prediction=int+cx*x_test+cy*y_test

Answer 2

OK, so values at time t-1 predict values at time t. That makes sense.

First you should decide whether you think these values are independent or not. Do the x predict the y or z at all? And, do you think just the previous 1 value is predictive, or the previous n?

Either way you could model this as a simple regression problem. What technique is best really depends on what you expect the relationship to be, and what these variables are; I am not sure that's given here.

For example if they're sensor values read fairly rapidly, and the sensor changes slowly, you'd expect some simple model like a moving average to do well. For other types of values this would not be predictive at all.

This looks like the Markov chain model, so you may look into that, but somehow I think it's over-general for what I think the problem is.