modelfitting.Rmd

<h4>Fitting a Model with \<code>R</code></h4>

The  R command <tt>lm()</tt> is used to fit linear models. Firstly the response variable $y$  is specified, then the predictor variable $x$.
<p>
The tilde sign is used to denote the dependent relationship (i.e. y depends on x). The regression coefficients are then determined.
<p>
<pre><code>
lm(Y~X) # y depends on X
</code></pre>

The output will include the formula, and two coefficient terms

<ul>
<li> The intercept estimate is recorded under $(Intercept)$
<li> The slope estimate is recorded under the name of the predictor variable (here : $X$ ).
</ul>	

<pre><code>
Call:
lm(formula = Y ~ X)

Coefficients:
(Intercept)            X
0.7812       0.8581
</code></pre>

A more detailed data output (i.e. more than just the coefficients) is generated in the form of a data object, using the <code>summary()</code> command.


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<h3>Linear regression model</h3>

We can draw a scatterplot to assess the relationship between X and Y.
The commmand we will use is plot.
<ul>
<li> To fit a linear model, the relevant r command is <code>lm()</code>.
  Lets save the output as a data object called <b><i>fit1</i></b>.

  <li><code>summary()</code> is a very useful command when using Linear models.
</ul>
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<h3>Fitting a Regression Model</h3>
A regression model is fitted using the <tt>lm()</tt> command.
<br>
Consider the response variable $F$ and predictor variable $C$.
<pre><code>
C=c(0,2,4,6,8,10,12) 
F=c(2.1,5.0,9.0,12.6,17.3,21.0,24.7)
Fit1=lm(F~C)
</code></pre>

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