regression_solution.pdf

# B obtain a point estimate of the expected number of

• 58

This preview shows pages 4–7. Sign up to view the full content.

b. Obtain a point estimate of the expected number of broken ampules when X = 1 transfer is made. c. Estimate the increase in the expected number of ampules broken when there are 2 transfers as compared to 1 transfer. d. Verify that your fitted regression line goes through the point (? ̅ , ? ̅ ). Q1.22) Plastic hardness. Refer to Problems 1.3 and 1.14. Sixteen batches of the plastic were made, and from each batch one test item was molded. Each test item was randomly assigned to one of the four predetermined time levels, and the hardness was measured after the assigned elapsed time. The results are shown below; X is the elapsed time in hours? and Y is hardness in Brinell units. Assume that first-order regression model (1.1) is appropria'te. a. Obtain the estimated regression function. Plot the estimated regression function and the data. Does a linear regression function appear to give a good fit here? b. Obtain a point estimate of the mean hardness when X = 40 hours. c. Obtain a point estimate of the change in mean hardness when X increases by 1 hour. Solution: ? ̅ = 28, ? ̅ = 225.5625 ∑ (? 𝑖 − ? ̅ ) 𝑛=120 𝑖=1 (? 𝑖 − ? ̅ ) = 2604 ∑ (? 𝑖 − ? ̅ ) 2 𝑛=120 𝑖=1 = 1280

This preview has intentionally blurred sections. Sign up to view the full version.

5 ∑ (? 𝑖 − ? ̅ ) 2 𝑛=120 𝑖=1 = 5443.938 ? 1 = ? 1 ̂ = (? 𝑖 − ? ̅ )(? 𝑖 − ? ̅ ) (? 𝑖 − ? ̅ ) 2 𝑛=120 𝑖=1 𝑛=120 𝑖=1 = 2.034375 ? 0 = ? 0 ̂ = ? ̅ − ? 1 ? ̅ = 168.6 ? ̂ = 168.6 + 2.034375 ? At X=40 ? ̂ = 168.6 + 2.034375 (40) = 249.975 Q1.24) Refer to Copier maintenance Problem 1.20. a Obtain the residuals 𝒆 𝒊 and the sum of the squared residuals ∑ 𝒆 𝒊 ? . What is the relation between the sum of the squared residuals here and the quantity Q in (1.8)? b. Obtain point estimates of 𝝈 ? and . In what units is 𝝈 expressed? ∑ ? 𝑖 2 = 3416.377 ∑ ? 𝑖 2 = ? 𝜎 2 ̂ = ∑ ? 𝑖 2 ? − 2 = 3416.377 43 = 79.45063 = ??? 𝜎 = √??? = √79.45063
6 Q1.25) (H.W) Refer to Airfreight breakage Problem 1.21. a. Obtain the residual for the first case. What is its relation to 𝒆 ? ? b. Compute ∑ 𝒆 𝒊 ? and MSE. What is estimated by MSE? Q1.26) (H.W) Refer to Plastic hardness Problem 1.22. a. Obtain the residuals ej. Do they sum to zero in accord with (1.17)? b. Estimate 𝝈 ? and . In what units is 𝝈 expressed? Q1.21) Solution (H.W) Airfreight breakage. A substance used in biological and medical research is shipped by airfreight to users in cartons of 1,000 ampules. The data below, involving 10 shipments, were collected on the number of times the carton was transferred from one aircraft to another over the shipment route (X) and the number of ampules found to be broken upon arrival (Y). Assume that first-order regression model (1.1) is appropriate. a. Obtain the estimated regression function. Plot the estimated regression function and the data. Does a linear regression function appear to give a good fit here? ? ̂ = 10.2 + 4.0? b. Obtain a point estimate of the expected number of broken ampules when X = 1 transfer is made. If X=1 Then ? ̂ = 10.2 + 4.0(1) = 14.20 c. Estimate the increase in the expected number of ampules broken when there are 2 transfers as compared to 1 transfer.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Spring '18
• Dr Ribble

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern