Iterative Methods—non-Linear ————————————–  

Gauss-Seidel can easily solve for a vector

Say we perform a linear least squares fit on the log of data such that and we know the constants .  What would be the “power fit” equivalent?

Iterative methods—Linear ———————————–  

What is the precise interpretation of a number in the structure matrix of the discriminant analysis output? 

What is l1-regularized logistic regression? What is the purpose of l1-regularization?

A researcher conducting a principal component analysis has obtained a KMO index of 0.65 and found that the significance level for Bartlett’s test of sphericity is 0.02. What is the null hypothesis associated with Bartlett’s test of sphericity? What, should the researcher conclude from the KMO index and significance level? Be as specific as possible in your answers.

Consider five objects measured on three variables (x1, x2, and x3) as shown below.  The current clusters are: Cluster 1 contains objects 1 and 5, and Cluster 2 contains objects 2, 3, and 4.  Perform an iteration of K-means by computing the current centroids (cluster centers) and the squared Euclidean distances from each object to the centroids and reassigning each object to its nearest cluster center. Show all of your work for computing the centroids and the distances. Object 1 2 3 4 5 x1 measure 12 3 10 2 2 x2 measure 3 9 2 10 7 x3 measure 3 5 6 1 9  

What is the precise interpretation of the bivariate (or Pearson) correlation measure between two variables x and y? How does a measure of partial correlation between the same two variables differ from this measure?

A sample of n = 5 objects are measured on two variables, x and y.  Their measurements are shown in the table below.  Compute the product-moment correlation coefficient between x and y. Be sure to show all necessary work. Object 1 2 3 4 5 x-measure 5 12 6 2 10 y-measure 9 6 7 14 4