Given problem illustrates the use of temperature data, and especially the numbers of Heating degree Days and the numbers of Cooling Degree Days (HDD and CDD for short), to predict the price of a commodity. The idea of this part of the project has its origin in a claim found in the introductory article written by Geoffrey Considine for the Weather Resource Center of the Chicago Mercantile Exchange website.

We first describe the data. They are contained in the text file corntemp.asc. Once opened in S-Plus, run it as a script, and an S-Plus object (a data frame to be specific) named CORNTEMP will be created. It is a 606 × 3 - matrix of numbers. Each row corresponds to a month, starting from July 1948 (the first row), and ending December 1998 (the last row). The first column gives the official price a farmer could get for a bushel of corn in Iowa that month. This variable is called MCorn for Monthly Corn price.

The second column gives the monthly average heating degree days in Des Moines as measured at the meteorological station of the airport. Heating Degree Days (HDD's) and Cooling Degree Days (CDD's) are discussed in details in Chapter 5. For the purposes of the present problem it is enough to know that the higher the temperature in the summer, the larger the number of CDD's and the smaller the number of HDD's, and the cooler the temperature, the larger the number of HDD's and the smaller the number of CDD's. The second column of the data matrix was computed by summing up the HDD's of the month, and dividing the total by the number of days in the month. This variable is called MDMHDD for Monthly Des Moines HDD. The third column gives the monthly CDD averages for Des Moines. They were computed in the same manner. This variable is called MDMCDD

NB: The data have been "cleaned" but there are still some "NA". Explain how you handle these entries

The goal of the problem is to predict the November and December prices of corn in Iowa from the summer temperatures in Des Moines as captured by the numbers of CDD's and HDD's

1. For each year between 1948 and 1998

• Extract the November price of corn in Iowa;
• Choose and compute regressor variables involving the values of MCorn, MDMHDD and MDMCDD up to (and possibly including) July of the same year but not later. You are allowed to use up to 4 variables (but remember that, as we repeated over and over, the smaller this number the better).

Once this is done, regress the November price of corn in Iowa on the regressor variables you chose according to the rules of the second item above. You are expected to perform three regressions, at least one of them being linear, and at least one of them being nonparametric. For each of these regressions, you need to give the list of the steps you take, and the parameters you use, so that your results can be reproduced. Also, in each case you will compute the proportion of the variance of the response variable explained by the regression.

2. Same question as above, replacing the November price of corn by the December price, and the July limit by August.