Appendix E — Matrix Exercises

Author

Affiliation

Sean Davis

University of Colorado
Anschutz School of Medicine

E.1 Data preparation

For this set of exercises, we are going to rely on a dataset that comes with R. It gives the number of sunspots per month from 1749-1983. The dataset comes as a ts or time series data type which I convert to a matrix using the following code.

Just run the code as is and focus on the rest of the exercises.

data(sunspots)
sunspot_mat <- matrix(as.vector(sunspots),ncol=12,byrow = TRUE)
colnames(sunspot_mat) <- as.character(1:12)
rownames(sunspot_mat) <- as.character(1749:1983)

E.2 Exercises

• After the conversion above, what does sunspot_mat look like? Use functions to find the number of rows, the number of columns, the class, and some basic summary statistics.

ncol(sunspot_mat)
nrow(sunspot_mat)
dim(sunspot_mat)
summary(sunspot_mat)
head(sunspot_mat)
tail(sunspot_mat)

• Practice subsetting the matrix a bit by selecting:
  • The first 10 years (rows)
  • The month of July (7th column)
  • The value for July, 1979 using the rowname to do the selection.

sunspot_mat[1:10,]
sunspot_mat[,7]
sunspot_mat['1979',7]

These next few exercises take advantage of the fact that calling a univariate statistical function (one that expects a vector) works for matrices by just making a vector of all the values in the matrix.

• What is the highest (max) number of sunspots recorded in these data?

max(sunspot_mat)

• And the minimum?

min(sunspot_mat)

• And the overall mean and median?

mean(sunspot_mat)
median(sunspot_mat)

• Use the hist() function to look at the distribution of all the monthly sunspot data.

hist(sunspot_mat)

• Read about the breaks argument to hist() to try to increase the number of breaks in the histogram to increase the resolution slightly. Adjust your hist() and breaks to your liking.

hist(sunspot_mat, breaks=40)

Now, let’s move on to summarizing the data a bit to learn about the pattern of sunspots varies by month or by year.

• Examine the dataset again. What do the columns represent? And the rows?

# just a quick glimpse of the data will give us a sense
head(sunspot_mat)

• We’d like to look at the distribution of sunspots by month. How can we do that?

# the mean of the columns is the mean number of sunspots per month.
colMeans(sunspot_mat)

# Another way to write the same thing:
apply(sunspot_mat, 2, mean)

• Assign the month summary above to a variable and summarize it to get a sense of the spread over months.

monthmeans = colMeans(sunspot_mat)
summary(monthmeans)

• Play the same game for years to get the per-year mean?

ymeans = rowMeans(sunspot_mat)
summary(ymeans)

• Make a plot of the yearly means. Do you see a pattern?

plot(ymeans)
# or make it clearer
plot(ymeans, type='l')