I. Download the dataset GAS_Future_2021_Oct15.csv from the course website, which contains the gas future prices on Oct 15, 2021. Conduct the following analysis parallel to what we did in class for gas future in Lect 9 and 10.
1. Perform polynomial LS regression with degree = 3, 6, 9, and 12 on the future prices. Plotthe scatterplot of future prices and superimpose the curves of fitted models.(cf. Lecture 9
P.9)
2. Determine the degree p via ANOVA and R2. Justify your choice.(cf. Lecture 9 P.10-11)
3. Use the selected model to predict the next 6 future prices and comment.(cf. Lecture 9 P.12)
4. Fit natural splines with df = 5,8,15 on the future prices. Plot the scatterplot of future prices and superimpose the curves of fitted models. (cf. Lecture 10 P.15)
5. Compare the fit of polynomial regression with degree = 9 and natural splines with df = 8 in terms of both fit and forecast. (cf. Lecture 10 P.16-17)
