Regression Line in Mathematica using FIT function

Question

I dont know if I am confused or if I am doing this incorrectly.

I have two data sets

 a={1,2,3,4,5}
 b={6,7,8,9,10}

Mathematica will translate the sets as

 a = {1,1},{2,2},{3,3},{4,4},{5,5}
 b = {1,6},{2,7},{3,8},{4,9},{5,10}

I want to do a scatter plot and find the regression line. I know how to do a scatter plot but I am not sure how to do a regression line for both data sets.

I looked around and it was suggested to me that I can use this

 regline = Fit[Join{a,b},{1,x},x]

 Show[ListPlot[{a,b}], Plot[{regline}, {x, 0, 10}]]

This works but the "Join" makes the data sets A and B like this

 {1,2,3,4,5,6,7,8,9,10}

and translates to this.

{1,1},{2,2},{3,3},{4,4},{5,5},{6,6},{7,7},{8,8},{9,9},{10,10}.

Wouldn't the regression line need to be figure out on the data sets

 {1,1},{2,2},{3,3},{4,4},{5,5}
 {1,6},{2,7},{3,8},{4,9},{5,10}

and not

 {1,1},{2,2},{3,3},{4,4},{5,5},{6,6},{7,7},{8,8},{9,9},{10,10}.

The regression line would be different for both.

Answer 1

Maybe this is what you are looking for:

a = {1, 2, 3, 4, 5};
b = {6, 7, 8, 9, 10};
data = Join[Transpose[{Range[Length[a]], a}], Transpose[{Range[Length[b]], b}]]
regline = Fit[data, {1, x}, x]
Show[ListPlot[data], Plot[{regline}, {x, 0, 10}]]

{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, {1, 6}, {2, 7}, {3, 8}, {4, 9}, {5, 10}}

{2.5 + 1. x}