I have the relationship between f and each of other five variables, the relationships are acquired by linear regression and are as follow
$f = a{\tiny1}x{\tiny1} + b{\tiny1}$
$f = a{\tiny2}x{\tiny2} + b{\tiny2}$
...
$f = a{\tiny5}x{\tiny5} + b{\tiny5}$
I am thinking since the regression is already done and all x variables are related to the same y, and the range of y and x are the same (ranging from 0 to 100). I can just add those five linear functions together and do a normalization or scaling. Then, by feeding the added-up function like
$f = $$\sum_{i=1}^5 (Ai*Xi + Bi)$
with $x{\tiny1}, x{\tiny2}, .., x{\tiny5}$, I can get only single one y value.
Can anyone tell is this way valid, if so, in my case a's range is [0, 1], however, for the intercept b, they are quite large, how can I do the normalization or scaling in order to obtain a valid and reliable value y?
Thanks for any help in advance.
It depends on the structure of your data. I.e., if you can view it as $n$ vectors of a kind $$ (y_i, x_{1i}, x_{2i}, ..., x_{ni}), \quad i=1,...,n $$ then a multiple linear model should fit to the task, namely $$ y=\beta_0 + \sum_{j=1}^5\beta_jx_j + \epsilon. $$ That you can estimate using any statistical software.