Create data vectors x1 and x2

Assignment Help Financial Management

Reference no: EM131231644

The goal of this problem is to illustrate one of the most important features of the projection pursuit regression: its ability to detect interactions between the regressor variables. We first show that the function f(x₁, x₂) = x₁x₂ is easily written in the form used by the projection pursuit algorithm

1. Determine µ, β₁ and β₂ so that the identity:

holds for all x^t = [x₁, x₂] with at 1 = [1, 1], = [1, -1] and φ₁(t) = t² and φ₂(t) = -t².

2. Create data vectors X1 and X2 of length n = 512 and with entries forming independent samples from the uniform distribution U(-1, +1) over the interval [-1, 1]. Create the vector Y according to the formula:

Where ? = { ?_j}_j=1,...512is a Gaussian white noise (i.e. a sequence of independent identically distributed normal random variables with mean zero) with standard deviation σ = .2. Give a scatterplot of Y against X1, and of Y against X2.

3. Run the projection pursuit algorithm to regress Y on X1 and X2 with a number of terms between min.term= 2 and max.term= 3. Produce scatterplots to visualize the graphs of the functions φ_j (t) found by the algorithm (if in doubt, read the on line help file for the function ppreg). Does that fit with the results of the computations done in question 1. above? Finally, do a scatterplot of Y versus Yˆ and another scatterplot of the residuals versus Yˆ and comment.

NB: recall that we use the notation t to denote the transpose of a vector or a matrix.

Reference no: EM131231644

Questions Cloud

Assess quality of fit by computing sum of square residuals : Assess the quality of the fit by computing the sum of square residuals. - Produce the plots of the first three additive terms in the projection pursuit regression formula.

Discuss the implications of these two estimates : Discuss the implications of these two estimates. How many collectors of 3 m × 10 m would be required to produce the energy for commuting with an all-electric car with 60% efficient batteries?

Social environment of workplace influences the performance : Check your understanding by matching some of the theories in the left-hand column below with the corresponding key contributor or key concepts in the right-hand column. Pioneer in illustrating how the social environment of the workplace influences th..

Describe a time when you were surprised by something : Describe a time when you were surprised by something that was considered popular but that was new to you. Analyze whether or not you consider yourself to be an active participant in popular culture. Explain your analysis.

Create data vectors x1 and x2 : Create data vectors X1 and X2 of length n = 512 and with entries forming independent samples from the uniform distribution.

What is the margin as a percentage of the mid-exchange rate : What is the margin as a percentage of the mid-exchange rate? What is the ask rate for CAD? What is the bid rate for CAD? What is the ask rate for GBP? What is the bid rate for GBP?

Describe the topic and summarize the scope : Describe the topic and summarize the scope of your paper. Be specific and to the point. This is an important part of a paper as it engages the reader and sets the tone of the paper.

What reduction in co2 generation did the program achieve : Assuming that imported oil cost $55 per barrel, how long did it take for the savings in import to equal the investment in the program?

Preparing adjusting and closing entries across two periods : Prepare journal entries to: - Accrue the salaries payable on December 31: - Close the Salaries Expense account on December 31.

User Account

All Pages