Problem 4.5 Open and run the (data) script file vineyard.asc to create the data set VINEYARD.

1. Superimpose (on the same plot) the scatterplot of nb and lugs90, the graph of the polynomial regression of lugs90 on nb with a polynomial of degree 3 and the graph of the polynomial regression (still of degree 3) of the column of 50 measurements obtained by removing the first row and the last row from lugs90 on the column of 50 values obtained by removing the first row and the last row from nb.

2. Same thing with the natural spline regression with degree of freedom df = 5.

3. Same question with the smoothing spline regression.

4. Still redo the same thing, but with the kernel regression with a normal kernel and a bandwidth equal to 5.

5. Compare the results obtained in questions 2 and 3 to the results obtained in questions 4 and 5. Explain which features of the regression algorithms are responsible for the differences.

NB: If you are not sure of what the spline regressions do, just compare the polynomial and the regression methods used in questions 2 and 5 respectively.

Among the other regression methods seen in the text, which methods would give results of the type obtained in questions 2 and 3 and which methods would give results of the type obtained in question 4 and 5?