The goal of this problem is to mimic the volatility ratio prediction experiment described in the text in order to predict the afternoon value of the volatility indicator. The data needed for this problem are contained in the data matrices MORN.mat and AFT.mat used in the text.
1. Give the two dimensional scatterplot of the morning volatility and arrival rate indicators. Plot a three-dimensional scatter plot of these two explanatory variables together with the afternoon volatility indicator, plot the result of the least squares linear regression, and explain the results by identifying overly influential data points.
2. Plot the regression surfaces obtained by kernel regression (use the Gaussian kernel and three bandwidths which you will choose carefully after standardizing the explanatory variables), and confirm the explanations given in question 1. Above
3. Remove the excessively influential measurements identified earlier, recompute the kernel regression on the remaining data, plot the new regression surface, and compute the residual sum of squares.
4. Perform a projection pursuit analysis of the reduced data set, plot the projection pursuit regression surface, compute the new residual sum of squares and compare them both with the results obtained in question 3. above.