how do i obtain the slope error formula?

Answer 1

I trust you're doing a linear regression (least squares). You'll get a regression formula y = a + bx.

If your data values are {(x,y)}; sumx and sumy are the sums of the x's and y's respectively; sumx2 and sumy2 are the sums of the respective squares; sumxy is the sum of the products.

The regression formulas are

b = (n sumxy - sum x sum y) / (n sumx2 - sumx^2)

a = (sumy - b sumx) / n

After you get the regression parameters a and b, calculate the standard error of estimate Syx with this formula:

Syx = sqrt[(sumy2 - a sumy - b sumxy) / (n - 2)]

Now you can get the standard error of the slope b with this formula:

Sb = Syx / sqrt(sumx2 - n xbar^2)

where xbar = sumx / n is the mean of the x values.

From that, you can establish confidence intervals for the slope b, e.g.,

b - 2 Sb < beta < b + 2 Sb

at the 95% confidence level, where beta is the true slope of the population data.

Answer 2

You're going to need more details.

I would have to guess the derivative of the error formula.

Answer 3

erf(t)=2/sqrt(pi)* integral of e^-(s^2)ds from 0 to t

I think d erf /dt = 2/sqrt(pi)*e^-(t^2) and that should be your slope