some minor updates and fixes

Author: mca91

03-ch3.Rmd

@@ -52,7 +52,7 @@ the sample mean of $Y$. Then again, we could use an even simpler estimator for $
 
 $$ Y \sim \chi_{12}^2 $$
 
-which is not too unreasonable as hourly income is non-negative and we expect many hourly earnings to be in a range of $5\unicode{0x20AC}\,$ to $15\unicode{0x20AC}$. Moreover, it is common for income distributions to be skewed to the right --- a property of the $\chi^2_{12}$ distribution. 
+which is not too unreasonable as hourly income is non-negative and we expect many hourly earnings to be in a range of $5$ Euro to $15$ Euro. Moreover, it is common for income distributions to be skewed to the right --- a property of the $\chi^2_{12}$ distribution. 
 
 ```{r, fig.align='center'}
 # plot the chi_12^2 distribution

04-ch4.Rmd

@@ -803,12 +803,12 @@ $$Cov(X,Y)=4.$$
 
 Formally, this is written down as
 
-\begin{align}
+\begin{equation}
   \begin{pmatrix}
     X \\
     Y \\
   \end{pmatrix}
-  \overset{i.i.d.}{\sim} & \ \mathcal{N} 
+  \overset{i.i.d.}{\sim} \ \mathcal{N} 
   \left[
     \begin{pmatrix}
       5 \\
@@ -819,7 +819,7 @@ Formally, this is written down as
       4 & 5 \\
     \end{pmatrix}
   \right]. \tag{4.3}
-\end{align}
+\end{equation}
 
 To carry out the random sampling, we make use of the function `r ttcode("mvrnorm()")` from the package `r ttcode("MASS")` [@R-MASS] which allows to draw random samples from multivariate normal distributions, see `?mvtnorm`. Next, we use `r ttcode("subset()")` to split the sample into two subsets such that the first set, `r ttcode("set1")`, consists of observations that fulfill the condition $\lvert X - \overline{X} \rvert > 1$ and the second set, `r ttcode("set2")`, includes the remainder of the sample. We then plot both sets and use different colors to distinguish the observations.
 

ITER.log

@@ -1,10 +1,8 @@
-np
 knitr
 usethis
 devtools
 readxl
 dplyr
-bindrcpp
 MASS
 kableExtra
 carData
@@ -19,9 +17,9 @@ ggplot2
 plotly
 mvtnorm
 stargazer
-Formula
 plm
 tidyr
+np
 rddtools
 dynlm
 urca
@@ -31,9 +29,3 @@ quantmod
 forecast
 orcutt
 nlme
-strucchange
-vars
-timeDate
-timeSeries
-fBasics
-fGarch