Multiple Linear Regressions with Identical Slopes Is it possible to impose an identical slope during a multiple linear regression?
See below I have 3 sets of data with a linear fit y=ax+b. I would like to simultaneously impose the same a (while minimizing the error) and let excel return the b values for the 3 lines.
Thank you very much for any pointers.

 A: This is something where you push Excel to its limits, you might consider using more advanced statistical tools (e.g. R). But the following procedure might do the trick:


*

*calculate the means of x- and y-values for all three data sets: $\bar{y}_i$, $\bar{x}_i$, $i=1,2,3$.

*standardize your three data sets by subtracting the x-mean from the x-values and the y-mean from the y-values. If you use the standardize formula from Excel, provide $1$ as standard deviation. This step centers your scatterplots around the origin of the plot (effectively forcing the intercept in the regression to be zero).

*now put the centered values from all three sets into one big set (concatenating all three sets of x-values and all three sets of y-values) into two new variables $x^{\ast}$ and $y^{\ast}$.

*do the linear regression for this large set $(x^{\ast}, y^{\ast})$: you get an intercept of zero (or very close to zero) and one (!) slope $m$ that should be the best fit (or very close to it?).

*the correct intercepts $c_i$ for the three original data sets are retrieved by solving $\bar{y}_i=\bar{x}_i\cdot m + c_i$ for $c_i$, where $\bar{y}_i$ and $\bar{x}_i$ are the calculated means for the data sets and $m$ is the fitted slope.


I'm not entirely sure if this all mathematically correct, but it should solve your problem with Excel's capability.
