For ryegrass that was not infected with endophyte the following data were observed:

(a) Plot a scatterplot of number of ryegrass plants versus the infestation rate.

(b) The relationship between infestation rate and number of ryegrass plants is clearly nonlinear. Look at the transformed variable y = loge(n + 1).
Plot y versus x on a scatterplot. Does this appear to be more linear?

(c) Find the least squares line relating y to x.

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

(e) Assume that the observed yi are normally distributed with mean αx¯ +
(xi − x¯) × β and variance equal to that calculated in part (b.) Find the posterior distribution of β|(x1, y1),...,(x20, y20). Use a normal (0, 12)
prior for β.