I'm not using R or any other stats framework, I'm trying to implement myself an algorithm to optimize the fitting curve and to calculate the EC50 confidence intervals.
Problem I have is my lack of knowledge in this field, so almost everything I find is to do it using R and for the rest appears to be different approaches so I don't know if its the correct one.
I think I did pretty well fitting the curve using the Gauss-Newton method, I plotted the curve and its looking good.
Trying to calculate EC confidence intervals using this formula:
SE = sqrt(SUM((Y-Y')^2)/(N-2))
Where N is my number of scores, Y actual score of sample data, and Y' the prediction.
About confidence interval formula:
CI = Y +- crit.tvalue * SE * sqrt( (1/N-2) + ((EC50-xm)^2/SSx) )
Where SE is the formula above for standard error, n-2 are deegress of freedom, EC50 is the approximated EC50 value for what I'm calculating the confidence interval, "xm" is the mean of all x values and SSx is:
Is it correct? If not, what is the best approach?