SS2864B, 2020 Assignment #2

SS2864B, 2020
Assignment #2 
Instructions Submit an electronic version (pdf, words, etc) of your solutions (appropriately
annotated with comments, plots, and explanations) to owl.
1. One of the most important tasks in using R is to read data from external sources into
R objects, so that you can perform calculations and produce graphics. If you have a
data set that you’re interested in, try reading it into R using the scan and read.table
functions. If you don’t have a file of data to read, you can use the write and write.table
(opposite of scan and read.table respectively) to produce one. Before you start, use ¿
help(scan) to find the detailed usage of the function scan, the same for other functions.
Once you know how to use these functions, try
(a) Create a vector and a data.frame objects in R. Make sure to have floating or real
numbers in your objects.
(b) Use write and write.table to export the two objects into two files.
(c) Use scan and read.table to import data sets in the two files back into R but two
different object names.
(d) Verify that they are the same.
2. Use R to identify the elements as well as their index(s) of the sequence {2
1
, 2
2
, . . . , 2
15}
that exceed the corresponding elements of the sequence {1
3
, 2
3
, . . . , 153}.
3. R functions dump and save can be used to save any R objects into files. Use ?dump
and ?save to find out how to use them. Please list the similarity and difference of dump
and save functions. Create a few R objects (more than one object) and dump (and save)
them into (two separate) file. Find a way to rename dumped (saved) objects. Then use R
function source (and load) to source (load) the file you just created. Again use ?source
and ?load to find out how to use them. Check if you get the same R objects back (need
to compare renamed R objects with ones sourced (loaded) from a file.
4. The R function cut can be used to cut numerical values into many levels. Please investigate its usage and use it to cut bmi in the dataset Pima.te (from library(MASS)) into
many categories. First use the values in http://en.wikipedia.org/wiki/Body mass index
to do the cut and the R function table to find their frequencies and plot it. Then cut
again with only three categories underweight, normal, overweight and redo the frequency
and plot.
5. Consider the pressure data frame. There are two columns - temperature and pressure.
(a) Construct a scatterplot with pressure on the vertical axis and temperature on the
horizontal axis. Are the variables related linearly or nonlinear?
(b) The graph of the following function passes through the plotted points reasonably
well:
y = (0.168 + 0.007x)
20/3
.
1
The differences between the pressure values predicted by the curve and the observed
pressure vales are called residuals. Here is a way to calculate them:
residuals <- with(pressure, pressure-(0.168+0.007*temperature)^(20/3))
Construct a normal QQ plot (adding a qqline) of these residuals and decide whether
they normally distributed or weather they follow a skewed distribution.
(c) Now, apply the power transformation y
3/20 to the pressure data values. Plot these
transformed values against temperature. Is a linear or nonlinear relationship evident
now?
(d) Calculate residuals for the difference between transformed pressure values and those
predicted by the straight line. Obtain a normal QQ plot (adding a qqline), and
decide whether the residuals follow a normal distribution or not.
6. Consider the pressure data frame again.
(a) Plot pressure against temperature, and use the following command to pass a curve
through these data:
curve((0.168+0.007*x)^(20/3), from = 0, to = 400, add = TRUE)
Note: You can use lines instead of curve.
(b) Now, apply the power transformation y
3/20 to the pressure data values. Plot these
transformed values against temperature. Use the abline function to pass a straight
line through the points.
(c) Add a suitable title to the graph. Also add a legend to indicate the straight line.
(d) Re-do the above plots, but use the mfrow function to display them in a 2x1 layout
on the graphics page. Repeat once again using a 1x2 layout.
2