This question concerns the coefficient of determination, of a linear regression of some raw data that is thought to depend on some raw data.  Consider that any fit we try to do gives an improvement over the straight average of the data.  How is bounded?

Say you have two equations

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