北大暑期课程《回归分析》(Linear-Regression-Analysis)讲义

Class 1: Expectations, variances, and basics of estimation

Basics of matrix (1)

I. Organizational Matters

(1)Course requirements:

1)Exercises: There will be seven (7) exercises, the last of which is optional. Each

exercise will be graded on a scale of 0-10. In addition to the graded exercise, an

answer handout will be given to you in lab sections.

2)Examination: There will be one in-class, open-book examination.

(2)Computer software: Stata

II. Teaching Strategies

(1) Emphasis on conceptual understanding.

Yes, we will deal with mathematical formulas, actually a lot of mathematical formulas. But, I do not want you to memorize them. What I hope you will do, is to understand the logic behind the mathematical formulas.

(2) Emphasis on hands-on research experience.

Yes, we will use computers for most of our work. But I do not want you to become a computer programmer. Many people think they know statistics once they know how to run a statistical package. This is wrong. Doing statistics is more than running computer programs. What I will emphasize is to use computer programs to your advantage in research settings. Computer programs are like automobiles. The best automobile is useless unless someone drives it. You will be the driver of statistical computer programs.

(3) Emphasis on student-instructor communication.

I happen to believe in students' judgment about their own education. Even though I will be ultimately responsible if the class should not go well, I hope that you will feel part of the class and contribute to the quality of the course. If you have questions, do not hesitate to ask in class. If you have suggestions, please come forward with them. The class is as much yours as mine.

Now let us get to the real business.

III(1). Expectation and Variance

Random Variable: A random variable is a variable whose numerical value is determined by the outcome of a random trial.

Two properties: random and variable.

A random variable assigns numeric values to uncertain outcomes. In a common language, "give a number". For example, income can be a random variable. There are many ways to do it. You can use the actual dollar amounts.

In this case, you have a continuous random variable. Or you can use levels of income, such as high, median, and low. In this case, you have an ordinal random variable [1=high,

2=median, 3=low]. Or if you are interested in the issue of poverty, you can have a dichotomous variable: 1=in poverty, 0=not in poverty.