Connect the Dots: Factor Analysis

Explore mean and median as central measures, and range as a spread indicator affected by outliers; learn variance, its standard deviation, and the n-1 denominator for sample estimates.

Explore how covariance describes how two variables deviate together and how the covariance matrix summarizes relationships among many variables, with diagonal variances and a symmetric structure.

Explore how covariance matrices capture relationships among variables and how correlation, covariance over standard deviations, measures relationships; independence yields zero correlation and the correlation matrix shows ones on the diagonal.

Explore how to choose directions that maximize data variation using principal components, projecting data onto orthogonal axes to reduce dimensions while preserving information.

Learn how principal components analysis transforms correlated variables into orthogonal components by maximizing variance, using eigenvectors and eigenvalues from eigen decomposition for regression.

Understand PCA results: principal components are orthogonal and ordered by variance, with eigenvalues showing each component’s share of variance. Use the scree plot elbow to decide which components to keep.

Use eigenvalues and eigenvectors to select principal components that explain most variance, and compute the first principal component as the dot product with its eigenvector.

Learn when to use principal component analysis to reduce correlated variables, guided by eigenvalues and the correlation matrix, and apply the 0.3 off-diagonal rule of thumb.

Analyze covariances and correlation matrices to build a multiple regression for Apple stock, then apply principal components analysis with eigen decomposition to determine key components.

Compute and evaluate the correlation matrix for a diverse stock dataset to assess inter-stock relationships, then decide on applying principal components analysis to guide factor analysis.

Learn how to perform eigen decomposition in Excel using VBA to compute principal components, eigenvalues, and eigenvectors from the covariance matrix, and assess variance explained to select key components.

Examine how principal components feed a regression model for Apple stock, highlighting the impact of standardization and how the first three PCs improve the model's R-squared.

Import a csv of securities, parse dates, and build a frame; compute returns by dividing by the previous day and subtracting one, then standardize with scale for principal components analysis.

Apply eigen decomposition to the standardized covariance matrix to obtain eigenvalues and eigenvectors, construct principal components, and use them to build a regression model for Apple stock.

Learn to perform PCA in R using a single package function. Compute eigenvalues, eigenvectors, and the explained variance (R-squared) from a covariance matrix.

Explore principal components analysis in Python by standardizing data, computing covariance and correlation matrices, deriving eigenvectors for the first three components, and applying linear regression assessed by R-squared.