0
$\begingroup$

I am sure that this is an easy question, but I am not able to figure it out.
Given an equation, with ($SD$=standard deviation):
$y=a(+/-SD)*x+b(+/- SD)$.
Given a specific value for $y$, how would I solve for $x$?
Thanks so much (I tried to google this, but I did not even know what terms to use)

Edit based on below comment:

I performed a linear regression where there was error associated with the variables (Deming regression?), the output was an equation of the above form. I would now like to use this to estimate the value of $x$ given $y$.

  • 0
    It's hard to understand what you mean here. I guess you have $y = ax + b$ where the fitted regression coefficients $a$ and $b$ have statistical error? Of course, we can just solve the linear equation for x to give $x = (y-b)/a.$ Is this what you wanted or did you have some kind of question about the error? – 2017-01-19
  • 0
    @spaceisdarkgreen sorry, you are correct. I performed a linear regression where there was error associated with the variables (Deming regression?), the output was an equation of the above form. I would now like to use this to estimate the value of $x$ given $y$. I imagine that this would result in a cerrtain error associated with $x$. Hope this clarifies some of the confusion. So given $y$, $x$ falls within a certain range with it's own mean and associated error? I also edited the question above. – 2017-01-19
  • 0
    The best estimate of $x$ is probably $(y-b)/a.$ To compute the standard deviation of this, you need to not only know the standard deviation of $a$ and $b$ but how they are correlated, so in general we need to know this as well. Also if you're trying to predict $x$ from $y,$ why didn't you run the regression the other way? If you do this, usually the literature on whatever regression you're running / the software package includes how to compute prediction intervals, which would be a measure of the error in the predictions the regression gives on new data. – 2017-01-19

0 Answers 0