Do dummy variables have variance?
The variance of the dummy variable will be equal to p times q where p is the proportion of total scores that are located in the one group and q = 1-p.
Can you log transform a dummy variable?
You cannot take the natural log of a dummy variable because ln(0) is undefined. Thus, you cannot create a completely double-log specification when you have dummy independent variables. What is usually done is to take the natural log of the Y and continuous X variables, leaving the dummy variables untransformed.
How to calculate the entries of the covariance matrix?
With the covariance we can calculate entries of the covariance matrix, which is a square matrix given by C i, j = σ ( x i, x j) where C ∈ R d × d and d describes the dimension or number of random variables of the data (e.g. the number of features like height, width, weight, …).
How to extract scaling matrix from covariance matrix?
What we expect is that the covariance matrix C of our transformed data set will simply be which means that we can extract the scaling matrix from our covariance matrix by calculating S = C and the data is transformed by Y = S X.
Is the covariance between two categorical variables zero?
If you have two categorical variables (say Male/Female and Treated/Not Treated ), then it’s certainly possible that the dummy representation between them are independent with ~zero covariance, but not necessarily the case. X, Y independent ⇒ c o v ( X, Y) = 0 regardless of the nature of random variables X and Y.
How is eigen decomposition related to the covariance matrix?
Eigen Decomposition of the Covariance Matrix Eigen Decomposition is one connection between a linear transformation and the covariance matrix. An eigenvector is a vector whose direction remains unchanged when a linear transformation is applied to it. It can be expressed as