Problem 1

Re-express the following expressions. In one case the expression may become significantly more complex.

1. 
2. 
3. 
4. 

Problem 2

Suppose that , and are variables and are constants. Using the equation compute the effect of changing from to , holding constant. Write in a logical form that makes it most apparent what differences are being computed.

Problem 3

Name two substantially different statistical tests that would be useful for the each of the following hypotheses, assuming that needed assumptions hold.

1. The population mean systolic blood pressure for treated and untreated patients is the same.
2. The population mean systolic blood pressure for patients on placebo, drug A, and drug B are all equivalent.
3. There is no association between systolic blood pressure and total serum cholesterol.
4. The chance of a patient getting a stroke is the same for both sexes. (extra credit)

Problem 4

A randomized clinical trial is done to compare two treatments. What role if any does prediction play in this study?

Problem 5

Do all calculations by hand or by using low-level software functions (i.e., do not use any regression functions or menus). Considering the following data:

x	1	2	3	4	5
y	98	198	315	380	530

1. Compute least squares estimates a and b for simple linear regression
2. Compute the predicted values and residuals from each observation
3. For the fitted a and b and for the 4 other combinations of them obtained by multiplying and dividing b by 0.9 and by adding and subtracting 10 from a, compute the fitting criterion. Describe the patterns you see in the various values of the criterion. You may want to define an R function in order to save work, e.g.:

sse <- function(x, y, a, b) { yhat <- a + b * x sum((y - yhat)^2) } x <- 1:5 y <- c(98,198,315,380,530) a <- ... b <- ... sse(x, y, a, b) sse(x, y, a-10, b) ...