e training and test errors for each choice. (b) Implement the LDA method and report its training and testing errors. Note: Before carrying out the LDA analysis, consider deleting variable 16 first from the data, since it takes constant values and may cause the singularity of the covariance matrix. In general, a constant variable does not have a discriminating power to sep

How can software randomization be achieved? What are the appropriate methods for resizing or shifting values generated by the rand function?

Let's revisit our first problem, where we want to set up a series of chess matches so we can rank six players in our class. As we did before, we will assume that everyone keeps their chess rating a private secret; however, when two players have a chess match, the person with the higher rating wins 100% of the time. But this time, we are only interested in identifying the BEST of these six players and the WORST of these six players. (We don't care about the relative ordering or ranking of the middle four players.) Your goal is to devise a comparison-based algorithm that is guaranteed to identify the player with the highest rating and the player with the lowest rating. Because you are very strong at Algorithm Design, you know how to do this in the most efficient way. Here are five statements. A. There exists an algorithm to solve this problem using 6 matches, but there does not exist an algorithm using only 5 matches. B. There exists an algorithm to solve this problem using 7 matches,...

programming alnguage its R project

How can we implement randomization in software? How should the sizes of the values returned by the rand function be adjusted?

Apply R to simulate a set of 100 numbers with standard deviation of 2 and mean of 20. List out the set of numbers.

Recall that the dot product of two vectors (1d matrices) produces a scalar value. The dot product is slightly confusing as the scalar value produced can have an arbitrary meaning that simply represents the mathematical operations of multiplying and summing. In other words, the dot product can simply represent the linear projection of vector onto the number line. This interpretation will be used repeatedly throughout machine learning as our main goal will be to take some features dotted with some weights/parameters. Once again, this can be though of as projecting our features onto a number line where the projection acts as our prediction! Keep this idea in mind as it might not make complete sense as of yet. It also important to know that the dot product can additionally take on other meanings such as a geometric meaning which represents how similar any two vectors are when projected onto one another. Meaning, how much one vector points in the direction of another. Given the following...