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fixed some issues regarding ttcode and expressions in legend
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03-ch3.Rmd

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# add a legend
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legend("topleft",
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legend = c("N(10,1)",
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expression(Y[1]),
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expression(bar(Y)[n == 5]~),
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expression(bar(Y)[n == 25]~)
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expression(Y[n == 1]),
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expression(bar(Y)[n == 5]),
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expression(bar(Y)[n == 25])
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),
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lty = c(2, 1, 1, 1),
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col = c("black","green", "steelblue", "red2"),

05-ch5.Rmd

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<tt>summary()</tt> reports the $p$-value of the test that the coefficient on <tt>(Intercept)</tt> is zero to to be <tt>< 2e-16</tt>. This scientific notation states that the $p$-value is smaller than $\frac{2}{10^{16}}$, so a very small number. The reason for this is that computers cannot handle arbitrary small numbers. In fact, $\frac{2}{10^{16}}$ is the smallest possble number <tt>R</tt> can work with.
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```
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The vector `r ttcode("CASchools\$D")` has the type `r ttcode("logical")` (to see this, use `r ttcode("typeof(CASchools$D)")`) which is shown in the output of `r ttcode("summary(dummy_model)")`: the label `r ttcode("DTRUE")` states that all entries `r ttcode("TRUE")` are coded as `r ttcode("1")` and all entries `r ttcode("FALSE")` are coded as `r ttcode("0")`. Thus, the interpretation of the coefficient `r ttcode("DTRUE")` is as stated above for $\beta_1$.
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The vector `r ttcode("CASchools$D")` has the type `r ttcode("logical")` (to see this, use `r ttcode("typeof(CASchools$D)")`) which is shown in the output of `r ttcode("summary(dummy_model)")`: the label `r ttcode("DTRUE")` states that all entries `r ttcode("TRUE")` are coded as `r ttcode("1")` and all entries `r ttcode("FALSE")` are coded as `r ttcode("0")`. Thus, the interpretation of the coefficient `r ttcode("DTRUE")` is as stated above for $\beta_1$.
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One can see that the expected test score in districts with $STR < 20$ ($D_i = 1$) is predicted to be $650.1 + 7.17 = 657.27$ while districts with $STR \geq 20$ ($D_i = 0$) are expected to have an average test score of only $650.1$.
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06-ch6.Rmd

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summary(mult.mod)
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```
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Again, the output of `r ttcode("summary(mult.mod)")` tells us that inclusion of `r ttcode("NS")` in the regression would render the estimation infeasible. What happened here? This is an example where we made a logical mistake when defining the regressor `r ttcode("NS")`: taking a closer look at $NS$, the redefined measure for class size, reveals that there is not a single school with $STR<12$ hence $NS$ equals one for all observations. We can check this by printing the contents of `r ttcode("CASchools\$NS")` or by using the function `r ttcode("table()")`, see `?table`.
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Again, the output of `r ttcode("summary(mult.mod)")` tells us that inclusion of `r ttcode("NS")` in the regression would render the estimation infeasible. What happened here? This is an example where we made a logical mistake when defining the regressor `r ttcode("NS")`: taking a closer look at $NS$, the redefined measure for class size, reveals that there is not a single school with $STR<12$ hence $NS$ equals one for all observations. We can check this by printing the contents of `r ttcode("CASchools$NS")` or by using the function `r ttcode("table()")`, see `?table`.
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```{r}
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table(CASchools$NS)

ITER.log

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_bookdown.yml

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_setup.Rmd

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docs/1-introduction.html

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<p>Most commonly we display R code together with the generated output in code chunks. As an example, consider the following line of code presented in chunk below. It tells <tt>R</tt> to compute the number of packages available on <tt>CRAN</tt>. The code chunk is followed by the output produced.</p>
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<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="1-introduction.html#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co"># check the number of R packages available on CRAN</span></span>
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<span id="cb1-2"><a href="1-introduction.html#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">nrow</span>(<span class="fu">available.packages</span>(<span class="at">repos =</span> <span class="st">&quot;http://cran.us.r-project.org&quot;</span>))</span>
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<p>Each code chunk is equipped with a button on the outer right hand side which copies the code to your clipboard. This makes it convenient to work with larger code segments in your version of <tt>R</tt>/<em>RStudio</em> or in the widgets presented throughout the book. In the widget above, you may click on <tt>R Console</tt> and type <code>nrow(available.packages(repos = "http://cran.us.r-project.org"))</code> (the command from the code chunk above) and execute it by hitting <em>Enter</em> on your keyboard.<a href="#fn2" class="footnote-ref" id="fnref2"><sup>2</sup></a></p>
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<p>Note that some lines in the widget are out-commented which ask you to assign a numeric value to a variable and then to print the variable’s content to the console. You may enter your solution approach to <tt>script.R</tt> and hit the button <em>Run</em> in order to get the feedback described further above. In case you do not know how to solve this sample exercise (don’t panic, that is probably why you are reading this), a click on <em>Hint</em> will provide you with some advice. If you still can’t find a solution, a click on <em>Solution</em> will provide you with another tab, <tt>Solution.R</tt> which contains sample solution code. It will often be the case that exercises can be solved in many different ways and <tt>Solution.R</tt> presents what we consider as comprehensible and idiomatic.</p>
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docs/1.2-a-very-short-introduction-to-r-and-rstudio.html

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<span id="cb6-2"><a href="1.2-a-very-short-introduction-to-r-and-rstudio.html#cb6-2" aria-hidden="true" tabindex="-1"></a>z <span class="ot">&lt;-</span> <span class="fu">seq</span>(<span class="at">from =</span> <span class="dv">1</span>, <span class="at">to =</span> <span class="dv">5</span>, <span class="at">by =</span> <span class="dv">1</span>)</span>
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<p>In the first line we use a function called <tt>seq()</tt> to create the exact same vector as we did in the previous section, calling it <tt>z</tt>. The function takes on the arguments <tt>from</tt>, <tt>to</tt> and <tt>by</tt> which should be self-explanatory.

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