A substance used in biological and medical research is shipped by air-freight 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 is appropriate.

i. 1 2 3 4 5 6 7 8 9 10
Xi. 1 0 2 0 3 1 0 1 2 0
Yi. 16 9 17 12 22 13 8 15 19 11

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 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 (X bar, Y bar)
e. Calcuate s.
f. Test the hypothesis that beta1=0, using alpha=0.05.