Linear Regression Confidence Intervals in SQL

Question

I use fairly straightforward SQL to calculate the regression (intercept and tilt) coefficients of some (x, y) data points using least squares. This gives me a good line of best fit data. However, we would like to see 95% and 5% confidence intervals for the line of best fit (curves below).

link text http://www.curvefit.com/2a03be60.gif

This means that the true line has a 95% probability of being below the upper curve and a 95% probability of being above the lower curve. How can I calculate these curves? I already read wikipedia etc. And I did some search queries, but I did not find any clear mathematical equations so that they could be calculated.

Edit: here is the gist of what I have now.

--sample data create table #lr (x real not null, y real not null) insert into #lr values (0,1) insert into #lr values (4,9) insert into #lr values (2,5) insert into #lr values (3,7) declare @slope real declare @intercept real --calculate slope and intercept select @slope = ((count(*) * sum(x*y)) - (sum(x)*sum(y)))/ ((count(*) * sum(Power(x,2)))-Power(Sum(x),2)), @intercept = avg(y) - ((count(*) * sum(x*y)) - (sum(x)*sum(y)))/ ((count(*) * sum(Power(x,2)))-Power(Sum(x),2)) * avg(x) from #lr 

Thanks in advance.

Answer 1

The equation for the width of the confidence interval as f (x) is given here in the section "Confidence Interval at Set Values"

http://www.weibull.com/DOEWeb/confidence_intervals_in_simple_linear_regression.htm

The page will also guide you through the calculation example.

Answer 2

Try this site and scroll down to the middle. For each point in your line of best fit, you know your Z, your sample size, and your deviation std.

http://www.stat.yale.edu/Courses/1997-98/101/confint.htm

Answer 3

@PowerUser: he needs to use equations for two variables, not for installations with one variable.

Matt: If I had an old textbook on statistics, I could tell you what you want; Unfortunately, I do not have it, and I do not have my notes from my high school course. On the other hand, from what I remember, he can only have material for the confidence interval of the slope of the regression line ...

In any case, this page, hopefully, will have some help: http://www.stat.yale.edu/Courses/1997-98/101/linregin.htm .