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Shown below are the number of galleys for a manuscript (X) and the dollar cost of correcting typographical errors (Y) in a random sample of recent orders handled by a firm specializing in technical manuscripts. Assume that the regression model Yi = (β1*Xi) + εi is appropriate, with normally distributed independent error terms whose variance is σ^2 = 16.
(Note that above, Xi means X sub i and the same goes for εi and Yi.)
The (Xi, Yi) are as follows:
1: (7, 128)
2: (12, 213)
3: (4, 75)
4: (14, 250)
5: (25, 446)
6: (30, 540)
What is the likelihood for the six Y observations for σ^2 = 16?
I know that in order to obtain the likelihood, I have to find the density of each observation, which is given by the equation:
1/(σsqrt( 2π))* exp(-1/2 ((Yi-β0- β1Xi)/ σ)
and then multiply them.
But what values do I have to use for β0 and β1?
Thanks for any help!
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