Please help with these questions!

1. It has been asserted that a lung function test is a proxy variable for respiratory capacity. Why is that the case?

2. Suppose you ask your subjects how much sleep they had the previous night. Why would this be a proxy measure for how much they slept? What is it a precise (non-proxy) test for?

3. Suppose a study of therapeutic effectiveness collects observations on 8 variables for a sample of 40 patients, but there are 3 missing observations on one of the variables.

(a) Why might it be advisable to impute those 3 missing observations? (The key word is "might".)

(b) If there are 20 missing observations on that variable, why in general would it be *less* advisable to conduct an imputation for them? What adjustment would need to be made if imputation is rejected?

4. Suppose a pharmaceutical company is testing a new drug on a sample of 400 patients. One of the responses it is measuring is white blood cell count. All but one of the observations is within the normal range, but that single outlier is disturbingly low. Is it good practice to include that outlier or eliminate it from the sample? Why?