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fix: chapter 3, ex13. fix for calling rnorm with variance instead of … #64

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fix: chapter 3, ex13. fix for calling rnorm with variance instead of … #64

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4 changes: 2 additions & 2 deletions ch3/applied.Rmd
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Original file line number Diff line number Diff line change
Expand Up @@ -408,7 +408,7 @@ suggests that there isn't a relationship between y and $x^2$.
----
```{r}
set.seed(1)
eps1 = rnorm(100, 0, 0.125)
eps1 = rnorm(100, 0, sqrt(0.125))
x1 = rnorm(100)
y1 = -1 + 0.5*x1 + eps1
plot(x1, y1)
Expand All @@ -424,7 +424,7 @@ As expected, the error observed in $R^2$ and $RSE$ decreases considerably.
----
```{r}
set.seed(1)
eps2 = rnorm(100, 0, 0.5)
eps2 = rnorm(100, 0, sqrt(0.5))
x2 = rnorm(100)
y2 = -1 + 0.5*x2 + eps2
plot(x2, y2)
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41 changes: 22 additions & 19 deletions ch3/applied.html
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Expand Up @@ -743,7 +743,7 @@ <h2>13g.</h2>
<div id="h.-1" class="section level2">
<h2>13h.</h2>
<pre class="r"><code>set.seed(1)
eps1 = rnorm(100, 0, 0.125)
eps1 = rnorm(100, 0, sqrt(0.125))
x1 = rnorm(100)
y1 = -1 + 0.5*x1 + eps1
plot(x1, y1)
Expand All @@ -754,19 +754,19 @@ <h2>13h.</h2>
## lm(formula = y1 ~ x1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.29052 -0.07545 0.00067 0.07288 0.28665
## Min 1Q Median 3Q Max
## -0.8217 -0.2134 0.0019 0.2061 0.8108
##
## Coefficients:
## Estimate Std. Error t value Pr(&gt;|t|)
## (Intercept) -0.9864 0.0113 -87.3 &lt;2e-16 ***
## x1 0.4999 0.0118 42.2 &lt;2e-16 ***
## (Intercept) -0.9615 0.0319 -30.1 &lt;2e-16 ***
## x1 0.4997 0.0335 14.9 &lt;2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.113 on 98 degrees of freedom
## Multiple R-squared: 0.948, Adjusted R-squared: 0.947
## F-statistic: 1.78e+03 on 1 and 98 DF, p-value: &lt;2e-16</code></pre>
## Residual standard error: 0.319 on 98 degrees of freedom
## Multiple R-squared: 0.694, Adjusted R-squared: 0.691
## F-statistic: 223 on 1 and 98 DF, p-value: &lt;2e-16</code></pre>
<pre class="r"><code>abline(lm.fit1, lwd=3, col=2)
abline(-1, 0.5, lwd=3, col=3)
legend(-1, legend = c(&quot;model fit&quot;, &quot;pop. regression&quot;), col=2:3, lwd=3)</code></pre>
Expand All @@ -775,7 +775,7 @@ <h2>13h.</h2>
<div id="i.-2" class="section level2">
<h2>13i.</h2>
<pre class="r"><code>set.seed(1)
eps2 = rnorm(100, 0, 0.5)
eps2 = rnorm(100, 0, sqrt(0.5))
x2 = rnorm(100)
y2 = -1 + 0.5*x2 + eps2
plot(x2, y2)
Expand All @@ -787,18 +787,21 @@ <h2>13i.</h2>
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.1621 -0.3018 0.0027 0.2915 1.1466
## -1.6434 -0.4268 0.0038 0.4123 1.6215
##
## Coefficients:
## Estimate Std. Error t value Pr(&gt;|t|)
## (Intercept) -0.9456 0.0452 -20.9 &lt;2e-16 ***
## x2 0.4995 0.0474 10.6 &lt;2e-16 ***
## (Intercept) -0.9230 0.0639 -14.45 &lt; 2e-16 ***
## x2 0.4993 0.0670 7.46 3.6e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.451 on 98 degrees of freedom
## Multiple R-squared: 0.532, Adjusted R-squared: 0.527
## F-statistic: 111 on 1 and 98 DF, p-value: &lt;2e-16</code></pre>
## Residual standard error: 0.638 on 98 degrees of freedom
## Multiple R-squared: 0.362, Adjusted R-squared: 0.355
## F-statistic: 55.6 on 1 and 98 DF, p-value: 3.62e-11</code></pre>



<pre class="r"><code>abline(lm.fit2, lwd=3, col=2)
abline(-1, 0.5, lwd=3, col=3)
legend(-1, legend = c(&quot;model fit&quot;, &quot;pop. regression&quot;), col=2:3, lwd=3)</code></pre>
Expand All @@ -812,12 +815,12 @@ <h2>13j.</h2>
## x 0.3926 0.6064</code></pre>
<pre class="r"><code>confint(lm.fit1)</code></pre>
<pre><code>## 2.5 % 97.5 %
## (Intercept) -1.0088 -0.9640
## x1 0.4764 0.5234</code></pre>
## (Intercept) -1.0249 -0.8981
## x1 0.4332 0.5661</code></pre>
<pre class="r"><code>confint(lm.fit2)</code></pre>
<pre><code>## 2.5 % 97.5 %
## (Intercept) -1.0352 -0.8559
## x2 0.4055 0.5935</code></pre>
## (Intercept) -1.0498 -0.7963
## x2 0.3664 0.6323</code></pre>
<p>All intervals seem to be centered on approximately 0.5, with the second fit’s interval being narrower than the first fit’s interval and the last fit’s interval being wider than the first fit’s interval.</p>
</div>
<div id="a.-6" class="section level2">
Expand Down