Rlabs/Rcode_regression.html at master · huebner/Rlabs · GitHub

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<title>Example of a linear regression analysis: </title>

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<h1>Example of a linear regression analysis: </h1>

<h1>Association of boiling point and pressure</h1>

<h2>M. Huebner 2014-03-24</h2>

<p>In the 1840s and 1850s a Scottish physicist, James D. Forbes, wanted to be able to estimate
 altitude above sea level from measurement of the boiling point of the water.
 He studied the relationship between boiling point and pressure. Forbes’ theory suggested
 that over the range of observed values the graph of boiling point versus the logarithm of
 pressure yields a straight line. Since the logs of the pressures do not vary much, all
 values of log(press) are multiplied by 100. This avoids studying very small numbers,
 without changing the major features of the analysis.<br/>
 <em>Reference: S. Weisberg. Applied Linear Regression. Wiley 2005.</em></p>

<pre><code class="r"># load the data and attcah the dataset
library(MASS)
data(forbes)

# Transform the pressure to 100*log(presure) useing a base 10 logarithm
forbes$hlpr &lt;- 100 * log10(forbes$pres)
forbes$boil &lt;- forbes$bp
</code></pre>

<p>Create a scatter plot of the predictor versus the response. </p>

<pre><code class="r">plot(hlpr ~ pres, data = forbes)
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-2"/> </p>

<p><strong>This looks like a reasonable linear relationship.</strong></p>

<p>Create summary statistics and calculate the correlation coefficient</p>

<pre><code class="r">summary(forbes$boil)
</code></pre>

<pre><code>##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
##     194     199     201     203     209     212
</code></pre>

<pre><code class="r">summary(forbes$hlpr)
</code></pre>

<pre><code>##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
##     132     136     138     140     144     148
</code></pre>

<pre><code class="r">cor(forbes$boil, forbes$hlpr)
</code></pre>

<pre><code>## [1] 0.9975
</code></pre>

<p>Fit a linear regression model and look at the regression output</p>

<pre><code class="r">fit &lt;- lm(hlpr ~ boil, data = forbes)
summary(fit)
</code></pre>

<pre><code>##
## Call:
## lm(formula = hlpr ~ boil, data = forbes)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -0.3197 -0.1471 -0.0689  0.0188  1.3599
##
## Coefficients:
##             Estimate Std. Error t value Pr(&gt;|t|)
## (Intercept) -42.1642     3.3414   -12.6  2.2e-09 ***
## boil          0.8956     0.0165    54.4  &lt; 2e-16 ***
## ---
## Signif. codes:  0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1
##
## Residual standard error: 0.379 on 15 degrees of freedom
## Multiple R-squared:  0.995,  Adjusted R-squared:  0.995
## F-statistic: 2.96e+03 on 1 and 15 DF,  p-value: &lt;2e-16
</code></pre>

<p><strong>The boiling point is a sigificant predictor for 100 log(pressure).</strong></p>

<p>Draw a scatter plot with the regression line.</p>

<pre><code class="r">plot(hlpr ~ pres, data = forbes)
abline(fit)
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-5"/> </p>

<p>Regression coefficients: this is the slope</p>

<pre><code class="r">fit$coefficients[2]
</code></pre>

<pre><code>##   boil
## 0.8956
</code></pre>

<p>Note that the estimated regression line is <code>hlpr=fit$coefficients[1]+fit$coefficients[2]*boil</code> namely  hlpr= -42.1642 + 0.8956 boil.</p>

<p>R square and adjusted R square indicate how much variation of the response (hlpr) is explained by regression on the boiling point.</p>

<pre><code class="r">summary(fit)$r.squared
</code></pre>

<pre><code>## [1] 0.995
</code></pre>

<pre><code class="r">summary(fit)$adj.r.squared
</code></pre>

<pre><code>## [1] 0.9946
</code></pre>

<p>How scattered are the points around the line?</p>

<pre><code class="r">summary(fit)$sigma
</code></pre>

<pre><code>## [1] 0.3792
</code></pre>

<p>Calculate a 95% CI for the slope</p>

<pre><code class="r">tble &lt;- summary(fit)$coefficients
slope.mean &lt;- tble[2, 1]
slope.se &lt;- tble[2, 2]
df &lt;- fit$df.residual
critval &lt;- abs(qt(0.025, df))

CIlow &lt;- slope.mean - critval * slope.se
CIup &lt;- slope.mean + critval * slope.se
</code></pre>

<p>A 95% CI for the slope is (0.8605, 0.9307).</p>

<p>Is the boiling point statistically significantly associated with HLPR?</p>

<pre><code class="r">pval &lt;- tble[2, 4]
</code></pre>

<p><strong>The p value for testing \( H_0: \beta = 0 \) vs \( H_1: \beta \ne 0 \) is 1.1898 &times; 10<sup>-18</sup>.</strong></p>

<h3>Diagnostics and Residual Analysis</h3>

<p>Is there evidence that the residuals do not follow a normal distribution?</p>

<pre><code class="r">qqnorm(fit$residuals)
qqline(fit$residuals)
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-11"/> </p>

<p><strong>It appears there is one outlier.</strong></p>

<p>Make a residual plot.</p>

<pre><code class="r">fit.stdres = rstandard(fit)
plot(fit$fitted, fit.stdres, xlab = &quot;Fitted values&quot;, ylab = &quot;Standardized residuals&quot;)
abline(h = 0, col = 2, lwd = 2)
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-12"/> </p>

<p>You can identify the point with the largest residual by using <code>identify(fit$fitted, fit.stdres)</code> click on the point in questions and then click Esc. This will identify the point as record number 12 in the dataset.</p>

<p>In the presence of outliers, it is useful to do the anlaysis with and without the point.
Remove large residuals.</p>

<pre><code class="r">indx &lt;- which(fit.stdres &gt; 2)
forbes1 &lt;- forbes[-indx, ]
</code></pre>

<p>Redo regression analysis with this outlier removed</p>

<pre><code class="r">fit1 &lt;- lm(hlpr ~ boil, data = forbes1)
summary(fit1)
</code></pre>

<pre><code>##
## Call:
## lm(formula = hlpr ~ boil, data = forbes1)
##
## Residuals:
##     Min      1Q  Median      3Q     Max
## -0.2088 -0.0634  0.0197  0.0884  0.1356
##
## Coefficients:
##              Estimate Std. Error t value Pr(&gt;|t|)
## (Intercept) -41.33468    1.00331   -41.2  5.2e-16 ***
## boil          0.89111    0.00494   180.2  &lt; 2e-16 ***
## ---
## Signif. codes:  0 &#39;***&#39; 0.001 &#39;**&#39; 0.01 &#39;*&#39; 0.05 &#39;.&#39; 0.1 &#39; &#39; 1
##
## Residual standard error: 0.114 on 14 degrees of freedom
## Multiple R-squared:     1,   Adjusted R-squared:     1
## F-statistic: 3.25e+04 on 1 and 14 DF,  p-value: &lt;2e-16
</code></pre>

<p><strong>The regression fit and coefficient of determination did not change much.</strong></p>

<pre><code class="r">fit.stdres = rstandard(fit1)
plot(fit1$fitted, fit.stdres, xlab = &quot;Fitted values&quot;, ylab = &quot;Standardized residuals&quot;)
abline(h = 0, col = 2, lwd = 2)
</code></pre>

<p><img 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" alt="plot of chunk unnamed-chunk-15"/> </p>

<p><strong>There are no obvious outliers in this plot after the point was removed.</strong></p>

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