Name: ________________________________________________
Course: GOVT 2302
Date: _________________________________________________
IN-CLASS EXERCISE #3 – Time Series, Standardized Scores
GENERAL INSRUCTIONS

This exercise will be completed in several parts. This is an individual assignment.
Please ask the instructor if you have questions.

Please be NEAT! The instructor will not grade illegible work.
Part 1.
1. Examine the table showing yearly data for two variable: presidential approval and
unemployment. The annual values of presidential approval are measured 12-month
averages. For example, the value indicated for 1953 (69%) is the average of the 12month period running from February 1953 – January 1954. The value for 1954
(64%) is the 12-month average for February 1954 – January 1955.
There are two exceptions: the first is the values for 1963 and 1964. John Kennedy
was assasinated in November 1963 so the value indicated for 1963 (63%) includes
Kennedy’s average approval rating from February 1963 – November 1963). The
value for 1964 (73%) is the average approval rating for Lyndon Johnson from
December 1963 – January 1965.
The second exception concerns the values for 1974 and 1975. Richard Nixon
resigned the presidency in the wake of the Watergate scandal in early August 1974.
Therefore, the value indicated for 1974 (28%) is Nixon’s monthly average for the
period running from February 1974 – July 1974. The value for 1975 (44%) is Gerald
Ford’s monthly average from August 1975 – January 1976.
The values for the unemployment variable are simply the 12 month averages running
from January – December of each year.
2. Complete the time series graph by plotting the values of presidential approval and
unemployment. Then, answer these questions:

How would you describe the behavior of the presidential approval variable over this
period (1953 – 2000)?

How would you describe the behavior of the unemployment rate over this period
(1953 – 2000)?

Based on your visual (ocular) examination of these two variables, can you conclude
that there is any relationship between the two? Explain.
Part 2.
One of the problems that we encounter in attempting to visual determine relationships
between time series is that the values of the variables are frequently quite divergent. For
example, the values of the presidential approval variable range from 28% to 73%.
Unemployment rates, on the other hand, range from just over 3% to just under 10%. As
a result, when the series are plotted on the same graph, the picture that emerges is
difficult to interpret. Is there a way to standardize the values of the variables so that any
relationship that might exist will become more apparent? The answer, fortunately, is:
yes.
The values of a variable are standardized according to the following simple process: [1]
compute the mean and standard deviation of each variable; [2] for each value of the
variable subtract the mean and then divide by the standard deviation. The standardized
values of a variable are referred to as the z-scores.
z = Xi – mean of X/standard deviation of X
The means and standard deviations of the presidential approval and unemployment
variables are provided in the table (bottom). The calculations for the first several years of
the series have already been completed.
1. Complete the table by calculating the z-scores for the remaining years of the series.
[Notice that the means of the standardized variables are equal to 0 (approximately)
and the standard deviations are equal to 1 (approximately). [They are standardized!]
2. Now plot the z-scores on the graph provided. Then, answer the following questions:

How would you describe the behavior of the standardized presidential approval
variable over this period (1953 – 2000)?

How would you describe the behavior of the standardized unemployment rate over
this period (1953 – 2000)?

Based on your visual (ocular) examination of these two variables, can you conclude
that there is any relationship between the two? Explain.

If you conclude that there is a relationship between the two variables, does it hold
perfectly throughout the series or are there notable exceptions to the relationship?
Explain. Identify the time periods that constitute exceptions to the relationship? Do
you know of anything (specific events, etc.) that might explain these exceptions. If
you conclude that there is no relationship between the two variables, explain why you
think this is the case.