# Linear regression

I have a sequence of data:

 data = {0.647888, 0.522495, 0.454224, 0.417054, 0.396816, 0.385798, 0.379799, 0.376532, 0.374754, 0.373786, 0.373259, 0.372972}


How can I find asymptote of this sequence using linear regression? Can anybody help me how to start? I just got a clue: y=a+b/c^x. Should I use LinearModelFit?

## 1 Answer

ClearAll[a, b, c]
data = {0.647888, 0.522495, 0.454224, 0.417054, 0.396816, 0.385798,
0.379799, 0.376532, 0.374754, 0.373786, 0.373259, 0.372972};

nlm = NonlinearModelFit[data, a + b/ c^x, {a, b, c}, x];
Normal@nlm


$0.372629\, +0.505569 \,\, 1.8367^{-x}$

Limit[Normal[nlm], x -> Infinity]


0.372629

• @hermano9, my pleasure. Thank you for the accept. – kglr Jun 12 '16 at 21:59
• This data set is clearly not from any biology experiment as a plot of the data and the fit shows almost no variability from the predicted model. An approximate 95% confidence interval for the value of the asymptote is found with nlm["ParameterConfidenceIntervals"][[1]] which shows as {0.372629, 0.372629}. – JimB Jun 12 '16 at 22:01