math stat Prerequisites Applied Regression Analysis Applied Regression Analysis 应用回归分析课件（英文版）.pdfVIP

Key Statistical and Mathematical Prerequisites NOTE TO THE STUDENT: This document is designed to review and re-instantiate previously acquired statistics knowledge. It is not designed to teach this material from scratch. If you aren’t familiar with the basic concepts, please consult your basic stats book. The purpose of this document is to review and introduce notation consistent with our course. A. Random Sample The basic building block of statistics is the random variable. A random variable is the quantifier of our world; it associates a number with each event in the world. A classic example of this is the number of heads in a sequence of 3 coin tosses. The events are the possible outcomes (e.g. HHH, HTH, TTH ...), the variable X defined as the number of heads in the sequence associates a real number with each event. Another example is the random variable H which represents the height of a person. Of course, a person is a complicated set of events (genetic inheritance, nutritional background ...). The H variable measures or quantifies only one aspect of this complicated set of outcomes that make-up the person. The height random variable has a probability distribution which is the distribution of all heights in the population. A random sample is a collection of independent and identically distributed random variables. { X , X , ... , X } are N iid r.v.s The important idea to remember here is 1 2 N that a random sample describes a mechanism for obtaining the data. The actual data we analyse is a realization or draw from the random sample. For example, if we draw one person out of N rooms in the building according to a random sample me