Let’s look at some basic commands in R.
Set up the following vector by cutting and pasting from this document:
a <- c(3,-7,-3,-9,3,-1,2,-12, -14)
b <- c(3,7,-5, 1, 5,-6,-9,16, -8)
d <- c(1,2,3,4,5,6,7,8,9)
Now figure out what each of the following commands do. You should not need me to explain each command, but I will explain a few. (more…)
In Part 7, let’s look at further plotting in R. Try entering the following three commands together (the semi-colon allows you to place several commands on the same line).
Let’s take an example with two variables and enhance it.
X <- c(3, 4, 6, 6, 7, 8, 9, 12)
B1 <- c(4, 5, 6, 7, 17, 18, 19, 22)
B2 <- c(3, 5, 8, 10, 19, 21, 22, 26)
In Part 6, let’s look at basic plotting in R. Try entering the following three commands together (the semi-colon allows you to place several commands on the same line).
x <- seq(-4, 4, 0.2) ; y <- 2*x^2 + 4*x - 7
plot(x, y) (more…)
In Part 3 and Part 4 we used the lm() command to perform least squares regressions. We saw how to check for non-linearity in our data by fitting polynomial models and checking whether they fit the data better than a linear model. Now let’s see how to fit an exponential model in R.
As before, we will use a data set of counts (atomic disintegration events that take place within a radiation source), taken with a Geiger counter at a nuclear plant.
The counts were registered over a 30 second period for a short-lived, man-made radioactive compound. We read in the data and subtract the background count of 623.4 counts per second in order to obtain
We were recently fortunate to host a free The Craft of Statistical Analysis Webinar with guest presenter David Lillis. As usual, we had hundreds of attendees and didn’t get through all the questions. So David has graciously agreed to answer questions here.
If you missed the live webinar, you can download the recording here: Ten Data Analysis Tips in R.
Q: Is the M=structure(.list(.., class = “data.frame) the same as M=data.frame(..)? Is there some reason to prefer to use structure(list, … ,) as opposed to M=data.frame?
A: They are not the same. The structure( .. .) syntax is a short-hand way of storing a data set. If you have a data set called M, then the command dput(M) provides a shorthand way of storing the dataset. You can then reconstitute it later as follows: M <- structure( . . . .). Try it for yourselves on a rectangular dataset. For example, start off with (more…)
In Part 2 of this series, we created two variables and used the lm() command to perform a least squares regression on them, treating one of them as the dependent variable and the other as the independent variable. Here they are again.
height = c(176, 154, 138, 196, 132, 176, 181, 169, 150, 175)
bodymass = c(82, 49, 53, 112, 47, 69, 77, 71, 62, 78)
Today we learn how to obtain useful diagnostic information about a regression model and then how to draw residuals on a plot. As before, we perform the regression.
lm(height ~ bodymass)
Call:
lm(formula = height ~ bodymass)
Coefficients:
(Intercept) bodymass
98.0054 0.9528
Now let’s find out more about the regression. First, let’s store the regression model as an object called mod and then use the summary() command to learn about the regression.
mod <- lm(height ~ bodymass)
summary(mod)
Here is what R gives you.
Call:
lm(formula = height ~ bodymass)
Residuals:
Min 1Q Median 3Q Max
-10.786 -8.307 1.272 7.818 12.253
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 98.0054 11.7053 8.373 3.14e-05 ***
bodymass 0.9528 0.1618 5.889 0.000366 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 9.358 on 8 degrees of freedom
Multiple R-squared: 0.8126, Adjusted R-squared: 0.7891
F-statistic: 34.68 on 1 and 8 DF, p-value: 0.0003662
R has given you a great deal of diagnostic information about the regression. The most useful of this information are the coefficients themselves, the Adjusted R-squared, the F-statistic and the p-value for the model.
Now let’s use R’s predict() command to create a vector of fitted values.
regmodel <- predict(lm(height ~ bodymass))
regmodel
Here are the fitted values:
1 2 3 4 5 6 7 8 9 10
176.1334 144.6916 148.5027 204.7167 142.7861 163.7472 171.3695 165.6528 157.0778 172.3222
Now let’s plot the data and regression line again.
plot(bodymass, height, pch = 16, cex = 1.3, col = "blue", main = "HEIGHT PLOTTED AGAINST BODY MASS", xlab = "BODY MASS (kg)", ylab = "HEIGHT (cm)")
abline(lm(height ~ bodymass))
We can plot the residuals using R’s for loop and a subscript k that runs from 1 to the number of data points. We know that there are 10 data points, but if we do not know the number of data we can find it using the length() command on either the height or body mass variable.
npoints <- length(height)
npoints
[1] 10
Now let’s implement the loop and draw the residuals (the differences between the observed data and the corresponding fitted values) using the lines() command. Note the syntax we use to draw in the residuals.
for (k in 1: npoints) lines(c(bodymass[k], bodymass[k]), c(height[k], regmodel[k]))
Here is our plot, including the residuals.
In part 4 we will look at more advanced aspects of regression models and see what R has to offer.
About the Author: David Lillis has taught R to many researchers and statisticians. His company, Sigma Statistics and Research Limited, provides both on-line instruction and face-to-face workshops on R, and coding services in R. David holds a doctorate in applied statistics.
See our full R Tutorial Series and other blog posts regarding R programming.