exercises 3

Author: jgscott

README.md

@@ -6,7 +6,7 @@ Some course logistics
 - Instructor: James Scott, <http://jgscott.github.com>  
 - Meets: Mondays and Wednesday, 1:00 to 2:30 PM
 - Classroom: UTC 4.120
-- Office hours: TBA
+- Office hours: Tuesday, 1-2 PM, via Zoom (link on Canvas).  Wednesdays in person, 2:30-3:30 PM, CBA 6.478.    
 
 ## Exercises 
 

data/greenbuildings.csv

@@ -28,6 +28,17 @@ Expected timeline:
 - By Feb 16: Fitting GLMs, A through C  
 - By Feb 21: Fitting GLMs, D through G  
 
+## Exercises 3: Bayes and the Gaussian linear model  
+
+The goals of [Exercises 3](exercises03-SDS383D.pdf) are: 
+- to introduce the normal/inverse-gamma conjugate prior for a location-scale model.    
+- to construct and fit a simple Bayesian linear model from scratch, based on normal/inverse-gamma conjugacy.  
+- to introduce hierarchical modeling, in the form of a regression model with heteroskedastic error.  
+
+Expected timeline TBA, but as a starting point:  
+- By Feb 23: aim to finish the section on "A simple Gaussian location model"  
+
+
 <!-- 
 ## Exercises 2: Bayes and the Gaussian linear model  
 

exercises/README.md

@@ -0,0 +1,12 @@
+a = 3
+NMC = 10000
+
+# Using the redundant parameterization
+tau = rnorm(NMC, 0, 1)*sqrt(1/rgamma(NMC, a/2, rate=a/2))
+
+hist(abs(tau), 500, prob=TRUE, xlim=c(0,5))
+curve(2*dt(x, a), add=TRUE)
+
+# Adding a mean
+tau = rnorm(NMC, 3, 1)*sqrt(1/rgamma(NMC, a/2, rate=a/2))
+hist(abs(tau), 500, prob=TRUE, xlim=c(0,5))

exercises/exercises03-SDS383D.pdf

@@ -0,0 +1,17 @@
+library(tidyverse)
+library(moderndive)
+
+greenbuildings = read.csv('../data/greenbuildings.csv')
+
+# Let's examine the "green premium"
+# starting point: define revenue per sq ft, as the rent times
+# the leasing rate (0-100 scale), divided by 100.
+# this is how much actual revenue the property brings in per square ft.
+greenbuildings = mutate(greenbuildings,
+                        rev_psf = Rent * leasing_rate/100)
+
+# using lm to get coefs and std. errors
+lm1 = lm(rev_psf ~ green_rating + City_Market_Rent + age + class_a + class_b, data=greenbuildings)
+
+# a regression table that I like better than "summary"
+moderndive::get_regression_table(lm1, conf.level = 0.95)