Eigenvalues of a Matrix and its Transpose are the Same

https://yutsumura.com/eigenvalues-of-a-matrix-and-its-transpose-are-the-same/

Recall that the eigenvalues of a matrix are roots of its characteristic polynomial.
Hence if the matrices A$A$ and AT$A^{\mathrm{T}}$ have the same characteristic polynomial, then they have the same eigenvalues.

So we show that the characteristic polynomial pA(t)=det(A−tI)$p_A(t)=det(A-tI)$ of A$A$ is the same as the characteristic polynomial pAT(t)=det(AT−tI)$p_{A^{\mathrm{T}}}(t)=det(A^{\mathrm{T}}-tI)$ of the transpose AT$A^{\mathrm{T}}$.

We have

pAT(t)=det(AT−tI)=det(AT−tIT)=det((A−tI)T)=det(A−tI)=pA(t).since IT=Isince det(BT)=det(B) for any square matrix B$$\begin{array}{rl}& p_{A^{\mathrm{T}}}(t)=det(A^{\mathrm{T}}-tI)\\ & =det(A^{\mathrm{T}}-t{I}^{\mathrm{T}})& & \text{since }{I}^{\mathrm{T}}=I\\ & =det\left((A-tI{)}^{\mathrm{T}}\right)\\ & =det(A-tI)& & \text{since }det(B^{\mathrm{T}})=det(B)\text{ for any square matrix }B\\ & =p_A(t).\end{array}$$

Therefore we obtain pAT(t)=pA(t)$p_{A^{\mathrm{T}}}(t)=p_A(t)$, and we conclude that the eigenvalues of A$A$ and AT$A^{\mathrm{T}}$ are the same.

Remark: Algebraic Multiplicities of Eigenvalues

Remark that since the characteristic polynomials of A$A$ and the transpose AT$A^{\mathrm{T}}$ are the same, it furthermore yields that the algebraic multiplicities of eigenvalues of A$A$ and AT$A^{\mathrm{T}}$ are the same.

Vanderbilt software carpentry bootcamps

Unix, Git, R and Python are taught

https://vanderbilt-data-science.github.io/2019-08-19-vanderbilt/

cellular aging

primary fibrablast in human
https://www.nature.com/articles/s41551-017-0093?fbclid=IwAR1BdQLw8HkiYfeunEp7I16sxUJkrQ-UydwWZgtpbkZ_w2Oe8jOkX3ODUBc

ROC

a perfect model has 100% sensitivity and specificity, a diagonal ROC line.

sensitivity: true positive rate, recall, probability of detection
specificity: true negative rate,

https://en.wikipedia.org/wiki/Sensitivity_and_specificity

logistic regression for binary dependent variables

https://www.statisticssolutions.com/what-is-logistic-regression/

What is Logistic Regression?

Logistic regression is the appropriate regression analysis to conduct when the dependent variable is dichotomous (binary).  Like all regression analyses, the logistic regression is a predictive analysis.  Logistic regression is used to describe data and to explain the relationship between one dependent binary variable and one or more nominal, ordinal, interval or ratio-level independent variables.

Sometimes logistic regressions are difficult to interpret; the Intellectus Statistics tool easily allows you to conduct the analysis, then in plain English interprets the output.

glm versus lm

I'm not satisfied with the answers here so I'll chime in: the model fit by lm is a special case of the model fit by glm.

lm fits models of the form: Y = XB + e where e~Normal( 0, s2 ).

glm fits models of the form g(Y) = XB + e, where the function g() and the sampling distribution of e need to be specified. The function 'g' is called the "link function". The default link function for glm is the "identity function" such that g(Y) = Y, and the default error distribution is Normal. As you can see, with these defaults glm is fitting the same model fit by lm.

The latter model above is a "generalized" linear model (hence "glm") in that the relationship between the regressors and the target is not strictly linear, but under a transformation (the link function) they are.

The most common glm's are poisson regression and logistic regression. Technically "normal" regression is the most common glm, but we generally don't refer to this as a "generalized" linear model, since it's the primary case upon which the general model is based.

TL;DR: The fact that you're getting the same answer is a good thing. It would be concerning if you weren't.