1 Introduction

Today you will get introduced to the R/RStudio environment, specifically working in the Console window. The Console window will display executed code output and can also be used for quick code execution. However, any work done in the Console window will be lost once you exit RStudio. As such, copy and paste the answer from the console in the script after each question.

2 Console computation

The console can be used as a calculator.

  • addition: +
  • subtraction: -
  • division: /
  • multiplication: *
  • modulus: %%
  • integer division: %/%
  • raise to power: ^

Evaluate the following expressions in the Console window

  1. 3 + 4 * 0 - (100 / 3)
    Answer: -30.33333

  2. (4 + 6) * (2 ^ 6)
    Answer: 640

  3. 1 / 0
    Answer: INF

  4. 10 ^ 10 ^ 10 ^ 10
    Answer: INF

  5. 0 / 0
    Answer: NaN

  6. 0.0000003 * 2
    Answer: 6e-07

When you launch R/RStudio numerous functions are immediately available to you. These include many of the mathematical and statistical operations you know.

R function Purpose
abs absolute value
sin sine
cos cosine
tan tangent
log logarithm
exp exponential
mean arithmetic mean
median median
sd standard deviation

Evaluate the following expressions in the Console window.

  1. absolute value of 7
    Answer: 7

  2. sine of 3.1415
    Answer: 9.265359e-05

  3. exponential 1
    Answer: 2.718282

  4. logarithm of 1, 6, 10
    Answer:0,1.791759,2.302585

What logarithm did you just take? Was it the natural log, base 10, base 2? natural log Type ?log in the console. Another way to access help is to use ?<functionname>. A question mark that precedes a function’s name or built in data object will open the help. (Note: put ?log in the console window).

Type the following in the Console window.

  1. ?sd - standard deviation
  2. ?mtcars -
  3. ?longley

What are mtcars and longley? mtcars = Motor Trend Car Road Tests longley = Longley’s Economic Regression Data

The most important aspects of R’s help resource will be the description and examples given. Examples are always at the end of the help reference.

  1. How many examples are given in the help of sd?
    Answer: 1

  2. Run the example provided in the help for sd in the console.
    Answer:0.5

Investigate what the following functions do:

  1. sqrt
    Answer: square root

  2. round
    Answer: rounds the number up or down

  3. floor
    Answer:Round Down

  4. ceiling
    Answer: Round up

3 Longley data

3.1 Examine the data

You just found out about the longley dataset. Consider Longley’s Economic Regression Data. This data set is built-in to R. That means it is available immediately once RStudio is launched. Type longley in your console to see the entire data set. The same data is given below.

Answer the following questions about the longley data set.

  1. How many rows and columns does longley have? Hint: check the nrow and ncol functions.
    Answer: 16 rows and 7 rows

  2. What is the difference between the first column of years and the column with the label Year?
    Answer: The column with the label has a int symbol underneath it

  3. Type head(longley) in the Console window. What does this do? How about tail(longley)?
    Answer: Head produces the first portion of the data and Tail produces the last bit of the data

3.2 Summary statistics

The data set longley is stored in R as a data frame. Each column is a vector of the same variable type. We will learn about these details later. For now, to access a specific vector use longley$variable_name, where variable_name is one of the variables in longley. For example,

longley$GNP
 [1] 234.289 259.426 258.054 284.599 328.975 346.999 365.385 363.112 397.469
[10] 419.180 442.769 444.546 482.704 502.601 518.173 554.894
longley$Year
 [1] 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961
[16] 1962

give the GNP and Year vectors of data.

In your Console window get the following vectors: Note: You need not include the output for the vectors in the script. Just write down the R code used for 4-6 below.

  1. Unemployed
    Answer: longley$Unemployed

  2. Population
    Answer: longley$Population

  3. Employed
    Answer: longley$Employed

In your Console window compute the mean, median, and standard deviation for each of the vectors in 4 - 6. Type in your answers below. Tip: You can press the up-arrow on your keyboard to cycle through previous inputs in the Console and use that for calculation.

  1. Unemployed
    Answer:Mean = 319.3313 median = 314.35 sd = 93.44642

  2. Population
    Answer: Mean = 117.424 Median = 116.8035 sd = 6.956102

  3. Employed
    Answer: Mean = 65.317 Median = 65.504 sd = 3.511968

Compute the maximum and minimum for each of the vectors in 4 - 6. Hint: check the min and max functions.

  1. Unemployed
    Answer: min = 187 max = 480.6
  2. Population
    Answer: min = 107.608 max = 130.081
  3. Employed
    Answer: min = 60.171 max = 70.551 The summary function in R will give you many of these statistics. For example,
summary(longley$GNP)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  234.3   317.9   381.4   387.7   454.1   554.9

gives us the minimum, maximum, mean, and quartiles of the GNP vector of data.

Use the summary function on two variables of your choice in longley. Do you think it makes sense to use the summary function on the variable Year in longley?
Answer: No it doesn’t make sense because those are years that increase one at a time so not any actual data

3.3 Employment investigation

Suppose it is 1962. Two economists are discussing employment. Each makes the following claim.

Economist A: The number of people employed has never been higher in the past 15 years. We have seen a gradual increase from 1947 to 1962.

Economist B: Employment has been range bound since 1947 and is at its lowest level since 1947.

Which economist is correct? Hint: Look at the variable Employed across time. To make a simple plot use the function plot. Create also a new variable, Employment, defined as Employed/Population and look at it across time.

plot(x = longley$Year, y = longley$Employed)

longley$Employment <- longley$Employed/longley$Population
plot(x = longley$Year, y = longley$Employment)

Answer: Economist A

The graphics don’t look as attractive. The plot function is part of the base R graphics and is used to make simple graphs. Later we will learn about more advanced graphics using the ggplot2 package. We will use the package extensively in the future. However, we can tidy the above plot with the following code.

plot(x = longley$Year, y = longley$Employed, xlab = "Year", ylab = "Employed")

Tidy up the second plot by changing the labels
Answer:

4 Essential details

4.1 Deadline and submission

The M1 ICA1 is an in-class group assignment. However, each member of the group who worked together in class will submit their in-class assignment at the end of the class time. Submit your work by uploading both your RMD and HTML files through D2L. Late work will not be accepted except under certain extraordinary circumstances.

4.2 Grading

To grade the ICAs, the instructional team will pick one submission at random from each group. Thus it is important that there is good intra- group communication and teamwork. Each group should ensure that everyone in the team understood, and completed the assignment.

5 References

  1. J. W. Longley (1967) An appraisal of least-squares programs from the point of view of the user. Journal of the American Statistical Association 62, 819-841.