This Course description: As a follow-up to the course Econ $120 \mathrm{~A}$, this course provides an introduction to the regression analysis frequently used in economics, business, and many other areas. It deals with applications of statistical methods for testing and estimation of causal relationships can be inferred from data. The material can be challenging and the workload is substantial. However, the payoff for this course is a set of skills and analytical tools that are very useful and in high demand in the marketplace.
这是一份UCSANDIEGO加利福尼亚大学圣迭戈分校UCSD 120B作业代写的成功案
Write out a population multivariate linear regression model where y is the PCR test result, and $x^{\prime} s$ include an indicator for symptomatic, an indicator for the spit test result and a separate indicator for spit test result for symptomatic patients.
PCR pos $=\beta_{0}+\beta_{1}$ Symptomatic $+\beta_{2}$ Spit pos $+\beta_{3}$ Symptomatic $x$ Spit pos $+u$
1B. What is the interpretation of the intercept in your population regression in (1A)?
The intercept is the predicted probability of testing positive on the PCR test for individuals who are asymptomatic and test negative on the spit test.
What is the numerical value of the predicted infection rate for a symptomatic individual with a positive spit test?
For that individual, Spit pos $=1$ Symptomatic $=1$ and Spit Symptomatic $=1$, so the predicted value is the sum of estimated coefficients $b_{0}+b_{1}+b_{2}+b_{3}=.176-.176+.449+.489=.938$
What is the numerical value of the predicted infection rate for an asymptomatic individual with a positive spit test?
For that individual, Spit pos $=1$ Symptomatic $=0$ and Spit Symptomatic $=0$, so the predicted value is the sum of estimated coefficients
$$
b_{0}+b_{1}+0+0=.176-.176=0
$$
CMTH110 COURSE NOTES ：
Definition 1.1. A statement (or proposition) is a sentence that is either true or false but not both.
Examples of statements:
- $p=$ “Alice is 12 years old”,
- $q=$ “Bob ate pizza for dinner yesterday”,
- $r=” 3 \cdot 3=9$ “,
- $s=” 2 \cdot 4=9 “$.
Examples of non-statements: - “Is the sky blue?” (question)
- ” $x^{2}+y^{2}=13 “$ (for some values of $x$ and $y$ the proposition is true, whereas for others it is false).
Compound Statements
We can make new statement from old ones using operators like “not”, “and”, “or”, “if then”. There are a few simple examples: - “Alice is not 12 years old” $(\sim p)$,
- “Bob ate pizza for dinner yesterday and $3 \cdot 3=9$ ” $(q \wedge r)$.
Compound statements (since they are (regular) statements as well) must have well-defined truth values – they must be either true or false. We can write down a table of truth values for compound statements based on the truth values of component statements.
Definition 1.2. The negation of a statement $p$ (denoted $\sim p$ ) is true if $p$ is false. If $p$ is true, then $\sim p$ is false.