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 Y[sub:rk98zp2h]i[/sub:rk98zp2h] = (?[sub:rk98zp2h]1[/sub:rk98zp2h]*X[sub:rk98zp2h]i[/sub:rk98zp2h]) + ?[sub:rk98zp2h]i[/sub:rk98zp2h] is appropriate, with normally distributed independent error terms whose variance is ?[sup:rk98zp2h]2[/sup:rk98zp2h] = 16.
The (X[sub:rk98zp2h]i[/sub:rk98zp2h], Y[sub:rk98zp2h]i[/sub:rk98zp2h]) are as follows:
1: (7, 128)
2: (12, 213)
3: (4, 75)
4: (14, 250)
5: (25, 446)
6: (30, 540)
What is the maximum likelihood for the six Y observations for ?[sup:rk98zp2h]2[/sup:rk98zp2h] = 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/(?sqrt( 2?))* exp(-1/2 ((Y[sub:rk98zp2h]i[/sub:rk98zp2h]-?[sub:rk98zp2h]0[/sub:rk98zp2h]- ?[sub:rk98zp2h]1[/sub:rk98zp2h]X[sub:rk98zp2h]i[/sub:rk98zp2h])/ ?)
and then multiply them.
But my question is, what values do I have to use for ?[sub:rk98zp2h]0[/sub:rk98zp2h] and ?[sub:rk98zp2h]1[/sub:rk98zp2h]?
The (X[sub:rk98zp2h]i[/sub:rk98zp2h], Y[sub:rk98zp2h]i[/sub:rk98zp2h]) are as follows:
1: (7, 128)
2: (12, 213)
3: (4, 75)
4: (14, 250)
5: (25, 446)
6: (30, 540)
What is the maximum likelihood for the six Y observations for ?[sup:rk98zp2h]2[/sup:rk98zp2h] = 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/(?sqrt( 2?))* exp(-1/2 ((Y[sub:rk98zp2h]i[/sub:rk98zp2h]-?[sub:rk98zp2h]0[/sub:rk98zp2h]- ?[sub:rk98zp2h]1[/sub:rk98zp2h]X[sub:rk98zp2h]i[/sub:rk98zp2h])/ ?)
and then multiply them.
But my question is, what values do I have to use for ?[sub:rk98zp2h]0[/sub:rk98zp2h] and ?[sub:rk98zp2h]1[/sub:rk98zp2h]?