Reference no: EM131231733
The data to be used in this problem are contained in the S-Plus script file crude.asc. Running this script will create the data frame CRUDE containing a numerical matrix with 3325 rows and 12 columns, and the numeric vector COma of length 3325.
In both data structures, each row corresponds to a date, the first one being 4/18/1989, and the last one being 8/12/2002. Each row of the vector COma contains the average of the crude oil spot price over the period of 5 days starting on (and including) the date indexing the row. Each row of the matrix CRUDE gives the prices of the 12 futures contracts of crude oil as traded the day before. Form a data frame TRGCRUDE and a vector TRGCOma with the first 2500 rows of CRUDE and COma respectively. You shall also need to form a data frame TSTCRUDE and a vector TSTCOma with the last 825 rows of CRUDE and COma respectively. The goal is to predict the values of the average spot price over the next five days from the prices of the crude oil futures contracts traded the day before, by fitting a regression model to the training data contained in the data sets TRGxxx, and using the model to compute predictions for the values of the response in the testing sample TSTCOma
Warning. For all the predictions considered in this problem, the figure of merit should be the square root of the mean squared error. It is very important that you explain your work in detail. In particular, explain your choices for the order of the models, the kernel functions, and the bandwidths you use.
1. Fit a least squares linear regression model for COma against the 12 explanatory variables given by the prices of the futures contracts the day before using the data in TRGCRUDE and TRGCOma, use this model to predict the values of COma in TSTCOma from the corresponding values of the explanatory variables, and compute the figure of merit.
2. Fit a projection pursuit regression model for COma against the 12 explanatory variables given by the prices of the futures contracts the day before using the data in TRGCRUDE and TRGCOma, use this model to predict the values of COma in TSTCOma from the corresponding values of the explanatory variables, and compute the figure of merit.
3. Perform the PCA of the data in TRGCRUDE, plot the first four loadings, give the proportions of the variance they explain, and compute the first two principal components.
4. Fit a one dimensional kernel regression model for COma against the first principal component using the data in TRGCRUDE and TRGCOma, use this model to predict the values of COma in TSTCOma from the corresponding values of the explanatory variables, and compute the figure of merit.
5. Fit a two dimensional kernel regression model for COma against the first two principal components using the data in TRGCRUDE and TRGCOma, use this model to predict the values of COma in TSTCOma from the corresponding values of the explanatory variables, and compute the figure of merit.
6. Compare the numerical results obtained with the various methods, and explain why they could have been expected.
|
Determine the work done by the ammonia
: Determine the work done by the ammonia by summing the area below the P-V process curve. As you plot it, P is the height and the change in volume is the base of a number of rectangles.
|
|
Knowledge is authentic and credible
: As a professional you should have the ability to discern if information/knowledge is authentic and credible. You should be able to decide if information/knowledge has relevance or has resonance. Discuss what attributes/qualities/skills that an operat..
|
|
Identify all the potential lawsuits
: Laura Beguiled and Spencer Lacey are famous movie stars, and they are planning to be married. One day, while standing in line at their local supermarket, they noticed Spenser’s picture on the cover of several magazines. When the police came and ascer..
|
|
Line authority is basic type of authority to carry out tasks
: Line authority is a basic type of authority to carry out tasks and give orders related to the organization's primary purpose. Staff authority is the right to advise or assist those with line authority. Functional authority if the right given by highe..
|
|
Compare numerical results obtained with the various methods
: Compute the first two principal components. - Compare the numerical results obtained with the various methods, and explain why they could have been expected.
|
|
Statements about the transportation and bullwhip effect
: Which of the following statements about the bullwhip effect is NOT true? Which of the following statements about the transportation problem is NOT correct?
|
|
Examine the individual organizations compensation challenges
: Examine the individual organization's compensation challenges and industry competition. As a team, you are required to develop an incentive plan that encourages an organizational culture.
|
|
Produce numerical evidence that variable age does not add
: Produce numerical evidence that the variable age does not add to the prediction of the variable points and/or the variable assists in the case of neural network regression.
|
|
Who is the current president of gallaudet
: What are your thoughts on the 2nd protest? Are your thoughts the same or different toward this protest compared with the 1st protest? Be sure to give details and thoroughly explain your reasoning - your response should be substantial.
|