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I have a comprehensive covariance matrix for variables y1 (dependent variable), x1, x2, x3 (independent variables) and the associated mean values for each variable. How can I perform multiple regression using only the covariance matrix and the mean values?
I’m not sure I understand your problem, but it seems like you’re trying to find a model of the form y1 = a1*x1 + a2*x2 + a3*x3. If so, then what you need to do is solve the following linear system:
C*a = d
where the elements of the C matrix are: c_ij = sum(x_i * x_j) and the elements of the d vector are d_i = sum(x_i * y1). This will give you the a1, a2, a3 coefficients you were looking for.