# matrix algebra

1. ### Trouble understanding univariate logistic regression using categorical data

Hello, I have a cancer dataset of 98 observations. Cancer detection rate was determined for 2 detection modalities (C and S). One of the independent variables of interest was a 3 tiered scoring system (possible scores: 3, 4, and 5). On univariate logistic regression, the score was...
2. ### Probability limit of ridge estimator mu hat

I have been working on the following question for a while but I stucked at a certain point. I have done part a and b and I found = (I_T + D'D)y where I_T is the identity matrix with dimension T, lambda is tuning parameter and D is the second order difference matrix which is a tridiagonal and...
3. ### Correct Cross Validation. How to calculate the projected R Squared or Residual Sum Sq

Hi, I have read into the subject of finding good estimators to determine the goodness of fit when the regression on a trainingset is projected on a testset (unseen data). I have found a lot of scientific papers but I get completely lost in terminologie and very complex equations I do not...
4. ### Showing Left Side to Right Side.

Let \mathbf x is a (p\times 1) vector, \mathbf\mu_1 is a (p\times 1) vector, \mathbf\mu_2 is a (p\times 1) vector, and \Sigma is a (p\times p) matrix. Now I have to show -\frac{1}{2}(\mathbf x-\mathbf\mu_1)'\Sigma^{-1}(\mathbf x-\mathbf\mu_1)+\frac{1}{2}(\mathbf...
5. ### Why does the determinant always equal zero for a matrix of consecutive numbers?

Hi. Why does the determinant always equal zero for a matrix of consecutive numbers? This applies whether the consecutive numbers are in the matrix starting from smallest to largest, or vice versa. It also applies irrespective of whether they are entered row then column or vice versa, which...