Publications by Xingbei Chen
Assignment 1
2E1. Which of the expressions below correspond to the statement: the probability of rain on Monday? (1) Pr(rain) (2) Pr(rain|Monday) (3) Pr(Monday|rain) (4) Pr(rain, Monday)/ Pr(Monday) Answer: (2) Pr(rain|Monday) & (4) Pr(rain, Monday)/ Pr(Monday) 2E2. Which of the following statements corresponds to the expression: Pr(Monday|rain)? (1) The prob...
5692 sym R (2630 sym/18 pcs) 6 img
Assignment #5
6E1. List three mechanisms by which multiple regression can produce false inferences about causal effects. # Multicollinearity, post-treatment bias and collider bias 6E2. For one of the mechanisms in the previous problem, provide an example of your choice, perhaps from your own research. # An example of multicollinearity is using both weight and ...
1230 sym R (3342 sym/26 pcs) 2 img
Assignment #4
5E1. Which of the linear models below are multiple linear regressions? \[\begin{align} {μ_i = α + βx_i} \tag{1}\\ μ_i = β_xx_i + β_zz_i \tag{2} \\ μ_i = β_xx_i + β_zz_i \tag{3} \\ μ_i = α + β(x_i − z_i) \tag{4} \\ μ_i = α + β_xx_i + β_zz_i \tag{5} \\ \end{align}\] #Models 2, 3 & 5 are the multiple linear regressions 5E...
4168 sym R (4253 sym/20 pcs) 2 img
Assignment #7
8E1. For each of the causal relationships below, name a hypothetical third variable that would lead to an interaction effect: Bread dough rises because of yeast. Education leads to higher income. Gasoline makes a car go. #1. Temperature #2. Major #3. Age of a car 8E2. Which of the following explanations invokes an interaction? Caramelizing o...
2548 sym R (4835 sym/26 pcs) 1 img
Assignment #6
7E1. State the three motivating criteria that define information entropy. Try to express each in your own words. #Motivating criteria that define information entropy should #1) be measured on a continuous scale such that the spacing between adjacent values is consistent #2) capture the size of the possibility space is the value scales with the ...
1547 sym R (2228 sym/13 pcs)
Assignment #8
9E1. Which of the following is a requirement of the simple Metropolis algorithm? The parameters must be discrete. The likelihood function must be Gaussian. The proposal distribution must be symmetric. #3. The proposal distribution must be symmetric 9E2. Gibbs sampling is more efficient than the Metropolis algorithm. How does it achieve this ext...
2336 sym R (6036 sym/27 pcs) 4 img
Assignment #9
11E1. If an event has probability 0.35, what are the log-odds of this event? p <- 0.35 p/(1-p) ## [1] 0.5384615 11E2. If an event has log-odds 3.2, what is the probability of this event? lo <- 3.2 lo/(1+lo) ## [1] 0.7619048 11E3. Suppose that a coefficient in a logistic regression has value 1.7. What does this imply about the proportional chang...
2148 sym R (3787 sym/17 pcs)