The dataset uswages is drawn as a sample from the Current Population Survey in 1988. Predict the wage from the years of education. (a) Make a plot of the two variables of interest that makes some effort to avoid the problems of overplotting. Repeat the plot but use a log scale for the response. (b) Compute the default smoothing spline fit and display on top of the data. Comment on the quality of the fit. (c) Compute the default lowess fit and display on the fit. Does this method work better than smoothing splines in this instance? (d) For each number of years of education, compute both the mean and the median wage. Construct a plot showing how these means and medians change with education. Which summary works better? (e) Instead of means and medians, compute the two quartiles and the median and display on top of the data. (This is a form of quantile regression). (f) Display the lowess fit on the log-transformed data. Do you think it is better to work on the log scale for this data