Shown below are the number of galleys for a manuscript (X) and the dollar cost of...

 

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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 Y₁ = B₁X₁ + ₁ is appropriate, with normally distributed independent error terms whose variance is o²=16. i: 1 2 3 4 5 6 12 4 14 25 30 7 Y₁ 128 213 75 250 446 540 a. State the likelihood function for the six Y observations, for ²-16. b. Evaluate the likelihood function for B₁ = 17, 18, and 19. For which of these B₁ values is the likelihood function largest. c. The maximum likelihood estimator is b₁ = [X; Y₁/ Xi. Find the maximum likelihood estimate. Are your results in part (b) consistent with this estimate? d. Using a computer graphics or statistics package, evaluate the likelihood function for values of B₁ between B₁, 17 and B₁. = 19 and plot the function. Does the point at which the likelihood function is maximized correspond to the maximum likelihood estimate found in part (c)? 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 Y₁ = B₁X₁ + ₁ is appropriate, with normally distributed independent error terms whose variance is o²=16. i: 1 2 3 4 5 6 12 4 14 25 30 7 Y₁ 128 213 75 250 446 540 a. State the likelihood function for the six Y observations, for ²-16. b. Evaluate the likelihood function for B₁ = 17, 18, and 19. For which of these B₁ values is the likelihood function largest. c. The maximum likelihood estimator is b₁ = [X; Y₁/ Xi. Find the maximum likelihood estimate. Are your results in part (b) consistent with this estimate? d. Using a computer graphics or statistics package, evaluate the likelihood function for values of B₁ between B₁, 17 and B₁. = 19 and plot the function. Does the point at which the likelihood function is maximized correspond to the maximum likelihood estimate found in part (c)?

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D c Assume L L ELi vyi Yi Yi B xi Ei B xi 62 128 213 75 Li L ... View the full answer