# How to find y values given x values and summary statistics on y

how do I find y values if I am given a list of data for the following variables x1, x2, x3...x11 and I am provided the y mean 0.010451 and the y standard deviation 0.004336?

I tried a multivariable regression.... y = b1x1+ b2x2+ b3x3...b11x11 then solve for the betas and setting objective to the provided mean value of y and set the constraint for the provided value of the standard deviation of y, that didn't work.

I've looked into unsupervised learning techniques which I believe might be a way to solve for the solution. Looking at PCA and using the PCA values to help solve for a beta. Solving for the correlation in the following equation:

http://www.stat.wmich.edu/s216/book/node126.html

Principal component mean is 0, in the above bX = 0 as the mean of a principal component is 0 thus a, the intercept is = to the mean of Y. Using solver for correlation on the former equation and using the standard deviation of PC1 (principal component 1) and standard deviation of Y produces a beta. Y= PC1*B + a However, this exercise does not seem to be meaningful because the standard deviation of x is so small and doesn't appear to do much switching the correlation.

Any insights would be great.

• If that is all you are given, then I don't think you can do this. Mar 3, 2018 at 16:00