I am trying using multivariate regression to play basketball. Specificlly, I need to, based on X, Y, and distance from the target, predict the pitch, yaw, and cannon strength. I was thinking of using multivariate regression with multipule variables for each of the output parameter. Is there a better way to do this?
Also, should I use solve directly for the best fit, or use gradient descent?
Multivariate regression is equivalent to doing the inverse of the covariance of the input variable set. Since there are many solutions to inverting the matrix (if the dimensionality is not very high. Thousand should be okay), you should go directly for the best fit instead of gradient descent.
n be the number of samples, m be the number of input variables and k be the number of output variables.
X be the input data (n,m)
Y be the target data (n,k)
A be the coefficients you want to estimate (m,k)
XA = Y
X'XA=X'Y
A = inverse(X'X)X'Y
X' is the transpose of X.
As you can see, once you find the inverse of X'X you can calculate the coefficients for any number of output variables with just a couple of matrix multiplications.
Use any simple math tools to solve this (MATLAB/R/Python..).