finding slope/inte​rcept/std.​deviation of replicates

how do i find the slope and intercept of replicates? so for each x-value i have, there would be more than 1 y-value (e.g. 6 y value for each x value)

how would i go about finding the slope and intercept of this? i am not allowed to just average out the y-values for each x-value. they call these replicates. Thanks!

[Sean de Wolski]

So robust estimation? Why can't you just average them?

Answer 1

[Tom Lane]

You can just include the x value once for each y value. If you're just talking about least squares coefficient estimation (no standard errors or the like), this will give the same answer as averaging out the y values.

>> x = [1 1 1 5 5 5 5]';
>> y = [1 2 3 10 15 20 25]';
>> p = polyfit(x,y,1)
p =
    3.8750   -1.8750
>> polyfit([1 5]',[2 17.5]',1)
ans =
    3.8750   -1.8750