Question 13

We want to explore the impact of drinking on brain size. From 12 randomly selected adult participants, their weekly alcohol consumption (X) and their brain volumes (Y) measured from their MRI scans were recorded. A simple linear regression mode is built as Y = A + BX.

From the sample data and the regression model, we computed the residual as SSR  =  65 ml^2. Please estimate the variance of the responses Yi  (i=1,..,12) with the sample data.

Please round your answer to one decimal place correctly.

4. In proof testing of circuit boards, the probability that any particular diode will fail is 0.01. Suppose a circuit board contains 300 diodes.
(a) How many diodes would you expect to fail on a circuit board, and what is the standard deviation of the number that are expected to fail?
(b) With Poisson distribution approximation, what is the (approximate) probability that at least one diode will fail on a randomly selected board? Round your answer to 2 decimal places.
(c) If ten boards are shipped to a particular customer, how likely is it that at least two of them will work properly? (A board works properly only if all its diodes work)