The data set cricketer (DAAG) holds information on British first-class cricketers with year of birth 1840–1960. The function gam() in the mgcv package can be used to fit GLM models that include...

The data set cricketer (DAAG) holds information on British first-class cricketers with year of birth 1840–1960. The function gam() in the mgcv package can be used to fit GLM models that include smoothing terms, with automatic choice of smoothing parameter. Use the following to model changes with year of birth, in the proportion of left-handers in the cricketer data:

(a) Is the assumption of independence between cricketers, for these data, reasonable?

(b) What might explain the clear dip in the proportion of left-handers with birth years in the decade or so leading up to 1934?

(c) Use the following to get estimates on the scale of the response, and plot the results:

Add confidence bounds to the plot.