Stat 500Midterm 2 — 12 November 2009page 0 of 11Please put your name on the back of your answer book.Do NOTput it on the front. Thanks.Do not start until I tell you to.•The exam is closed book, closed notes. Use only the formula sheet and tables I provide today.You may use a calculator.•Write your answers in your blue book. Ask if you need a second (or third) blue book.•You have 2:15 hours (135 minutes) to complete the exam.Stop working when the end of the exam is announced.•Points are indicated for each question. There are 130 total points.•Important reminders:–budget your time. Some parts of each question should be easy; others may be hard. Makesure you do all parts you can.–notice that some parts do not require any computations.–show your work neatly so you can receive partial credit.•Good luck!
Stat 500Midterm 2 – 12 November 2009page 1 of 111. 50 points. Health of factory workers. The following data were collected in a study of the healthof paint sprayers in an auto assembly plant. Two of the variables that were measured on eachof the 103 workers in the study were H, the haemoglobin concentration, and L, the lymphocytecount. These are measures of two different components of the blood.The following quantities may help you answer the questions:The observed intercept and slope in the regressionHi=β0+β1Li+iareb0=-55.6,b1= 1.98The estimated s.d. of observations around the line isse= 4.95The error SS for the “intercept only” modelHi=μ+iis 8050.2The error SS for the regressionHi=β0+β1Li+iis 2474.2The error SS for the regressionHi=β0+β1Li+β2L2i+iis 2470.8The error SS for the regressionHi=β0+β1Li+β2L2i+β3L3i+iis 2396.4The error SS for the loess regressionHi=f(Li) +iis 2391.4 with 97.5 d.f.The mean lymphocyte count is 30.9.The sum-of-squares of lymphocyte counts,∑(xi-x)2, = 1428.The correlation coefficient between H and L is 0.838.(a) What statistic is the most appropriate to describe the association between haemoglobinconcentration and lymphocyte count? You may answer with one of the values I’ve provided,or some other statistic. Briefly explain why you chose your statistic.No matter how you answered the previous question, the investigators want you to fit the regres-sion:Hi=β0+β1Li+i.(b) Calculate the s.e. ofb1(c) Test H0:β1= 0. Report your test statistic and two-sided p-value.Note: If you were not able to do the previous question and need a s.e. for your test, uses.e.= 0.49.(d) The usual ANOVA table for this regression has rows and columns labelled:Sourced.f.SSMSFModel????????Error??????Total????Calculate as many of the missing entries as you can from the available data and what youknow about the study.(e) The investigators use the fitted regression to predict average haemoglobin concentration atthree possible lymphocyte counts:Li= 26,Li= 32, andLi= 35. Which prediction is themost precise? Explain your choice.
Stat 500Midterm 2 – 12 November 2009page 2 of 11(f) Here are a residual plot and a normal quantile-quantile plot for the fitted regression. Listthe assumptions made in the regression, then assess each using the information in the plots.