R Tip: Linear Regression

Anonymous

October 05, 2016

Linear Regression is a common statistical tool used to determine relationships between data This RTip is modified from: http://www.apsnet.org/edcenter/advanced/topics/EcologyAndEpidemiologyInR/DiseaseProgress/Pages/LinearRegression.aspx

install.packages("stats")

## Error in install.packages : Updating loaded packages

library(stats)

For example, let’s look at the relationship between girth and height of black cherry trees First, look at the data

head(trees)

##   Girth Height Volume
## 1   8.3     70   10.3
## 2   8.6     65   10.3
## 3   8.8     63   10.2
## 4  10.5     72   16.4
## 5  10.7     81   18.8
## 6  10.8     83   19.7

plot(trees$Girth, trees$Height, ylab = "Height", xlab = "Girth", pch=21, bg="royalblue")

Next, run the linear model

trees.lm<-lm(trees$Height~trees$Girth, data=trees)

And view the stats

summary.lm(trees.lm)

## 
## Call:
## lm(formula = trees$Height ~ trees$Girth, data = trees)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.5816  -2.7686   0.3163   2.4728   9.9456 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  62.0313     4.3833  14.152 1.49e-14 ***
## trees$Girth   1.0544     0.3222   3.272  0.00276 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.538 on 29 degrees of freedom
## Multiple R-squared:  0.2697, Adjusted R-squared:  0.2445 
## F-statistic: 10.71 on 1 and 29 DF,  p-value: 0.002758

The linear fit line has an intercept of 62.0313, an slope of 1.0544, and an R2 value of 0.2697

#Finally, add the linear fit line
plot(trees$Girth, trees$Height, ylab = "Height", xlab = "Girth", pch=21, bg="royalblue")
abline(trees.lm, col="black", lty=1)

save.image("Lab4RTip.RData")