The Elements of Multi-Variate Analysis for Data Science

These lecture notes provide a quick review of basic concepts in statistical analysis and probability theory for data science. We survey general description of singleand multi-variate data, and derive regression models by means of the method of least squares. As theoretical backgrounds we provide basic knowledge of probability theory which is indispensable for further study of mathematical statistics and probability models. We show that the regression line for a multi-variate normal distribution coincides with the regression curve defined through the conditional density function. In Appendix matrix operations are quickly reviewed. These notes are based on the lectures delivered in Graduate Program in Data Science (GP-DS) and Data Sciences Program (DSP) at Tohoku University in 2018–2020.