Sounds like a homework question ...
 
if y = a + bx + e,  where e ~ N(0, sigma^2)
 
the log likelihood of the slope parameter and intercept parameters, a and b, and variance sigma^2 given n data points y and covariates x is
 
f(a,b, sigma; y, x) = -0.5*n*log(2 * pi) - n*log(sigma) - 0.5 / sigma^2 * sum_i [ (y_i - (a + b*x_i))^2 ]
 
You can simplyfiy this function if you condition on the variance and intercept.  
You are then left with a simple function coresponding to the log-likelihood curve.
This function is trivial to minimise.
 
Hope this helps.
Colin.
 

________________________________

From: r-help-bounces@r-project.org on behalf of mat7770
Sent: Sun 08/11/2009 19:12
To: r-help@r-project.org
Subject: [R] negative log likelihood




I have two related variables, each with 16 points (x and Y). I am given
variance and the y-intercept. I know how to create a regression line and
find the residuals, but here is my problem. I have to make a loop that uses
the seq() function, so that it changes the slope value of the y=mx + B
equation ranging from 0-5 in increments of 0.01. The loop also needs to
calculate the negative log likelihood at each slope value and determine the
lowest one. I know that R can compute the best regression line by using
lm(y~x), but I need to see if that value matches the loop functions.
--
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