====== Correlation ======

In R, basic correlation tests are executed with two commands: ''cor()'' and ''lm()'' (where ''lm'' stands for linear model).

===== Calculating correlation =====


To calculate product moment correlation coefficient between ''Maxle'' and ''Maxwi'' for bronze spears:

<code C>
> Bronze = subset(spearhead, subset=Mat=="1")
> cor(Bronze$Maxle, Bronze$Maxwi)
[1] 0.6892216
</code>

To calculate Spearman's rank correlation coefficient between ''Date'' and ''Weight'' for bronze spears:

<code C>
> cor(Bronze$Date, Bronze$Weight, method="spearman")
[1] 0.1269293
</code>

===== Plotting correlation =====


To draw a scatterplot for ''Maxle'' and ''Maxwi'':

<code C>
> plot(Bronze$Maxle, Bronze$Maxwi)
</code>

The scatterplot by itself is already interesting, but R gives us another interesting function with the ''lm()'' command (where ''lm'' stands for //linear model//).

<code C>
> result <- lm(Bronze$Maxwi ~ Bronze$Maxle)
> result

Call:
lm(formula = Maxwi ~ Maxle)

Coefficients:
(Intercept)        Maxle  
     1.5053       0.1277  

</code>

  - note that the order of arguments to ''lm()'' is inverse: the basic use is ''lm(y ~ x)'' (with ''y'' as //dependent// variable)
  - the result of ''lm()'' is... a rect. You can see by yourself //plotting// it over the scatterplot

<code C>
> abline(result$coefficients, col="blue")
</code>

{{ :diggingnumbers:lm1.png |The composition of scatterplot and linear model}}

Plotting the ''lm()'' result by itself like

<code C>
> plot(result)
</code>

gives you more informative graphs about the linear model, but their content is beyond the scope of this tutorial.

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[[Start]] · [[Data description]] · [[Transforming variables]] · [[Tables]] · [[Pictorial displays]] · [[Measures of position and variability]] · [[Sampling]] · [[Tests of difference]] · [[Tests of distribution]] · **Correlation** · [[Tests of association]]