A researcher is investigating the relationship between fuel economy and driving speed. He makes six runs on a test track, each at a different speed, and measures the kilometers travelled on one liter of fuel. The speeds (in kilometers per hour)

and distances (in kilometers) are recorded below:

(a) Plot a scatterplot of distance travelled versus speed.

(b) Calculate the parameters of the least squares line.

(c) Graph the least squares line on your scatterplot.

(d) Calculate the estimated variance about the least squares line.

(e) Suppose that we know distance travelled given the speed is normal (α0 +
β × x, σ2) where σ2 = .572 is known. Use a normal (0, 12) prior for β.
What is the posterior distribution of β?

(f) Perform a Bayesian test of H0 : β ≥ 0 versus H1 : β < 0 at the 95 % level of significance.