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CHAPTER 15 SOLUTIONS AND MINI-PROJECT NOTES
CHAPTER 15
UNDERSTANDING AND REPORTING TRENDS OVER TIME
EXERCISE SOLUTIONS
15.1
a. Positive.
b. Nonexistent.
c. Negative.
d. Positive.
15.2
a.
b.
c.
d.
15.3
A trend would indicate global warming. Seasonal effects would be easy to separate out, but long cycles
might lead to an erroneous conclusion that there was global warming. That's why it's important to examine
data for as many years as possible when making this assessment.
15.4
It would be better to adjust for inflation to have a fair comparison over the years.
15.5
Divide the cost each year by the Consumer Price Index for that year.
15.6
You should plot the rate of homicides. Divide the number of homicides by the population first. Otherwise,
an increasing number of homicides could simply be due to the increase in population. An increase in the
rate would reflect a true increase in severity of the problem.
15.7
Because the population is constantly increasing, all statistics related to those kinds of events are also likely
to increase. Those increases do not reflect a meaningful change, however, and an increase or decrease in
rate is what matters.
15.8
You would expect a positive correlation because the regression line for the trend would have a positive
slope.
15.9
Major wars tend to cause upward cycles in economic time series. In other words, they are good for the
economy.
15.10
a. Seasonal and cycles.
b. Trend and seasonal. (The upward trend was certainly present as of 1995, but may or may not apply
now. Adjust the answer accordingly.)
c. Possible seasonal and cycles. For the seasonal, they may offer attractive rates at certain times of the
year, like when college students have just moved to the area and may be looking for a bank.
15.11
The seasonal component is likely to be the strongest because prices of major items like fresh foods and
energy tend to be seasonal. That's why the CPI is seasonally adjusted. (It is only in periods of very high
inflation that the trend might contribute more.)
15.12
For both of these pictures, make sure the time covered is many years. You cannot determine whether or not
seasonal components are present in a plot of only one or two years. An example for part a would be the
price of any item that doesn't change seasonally. An example for part b would be temperature measured
monthly in a city with real seasons (although some might argue that there are cycles present if you look long
enough).
15.13
The seasonal fluctuations in many time series would far outweigh the small changes from month to month,
but it is those changes that help indicate the health of the economy.
No seasonal component.
A definite seasonal component.
A possible seasonal component, with sales around Christmas.
A definite seasonal component with peaks around Christmas and the beginning of the school year.
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CHAPTER 15 SOLUTIONS AND MINI-PROJECT NOTES
15.14
Ask the boss to examine records from previous years to see if the drop is consistent with a yearly seasonal
component.
15.15
a. The 1994 salary would be $49,100 × (148.4/60.9) = $119,646, which is almost exactly equal to the
actual salary of $120,000.
b. The 1994 salary would be $200,000 × (148.4/60.9) = $487,356 so it certainly doesn't seem fair that it
was still only $200,000 in 1994.
15.16
Adjusting for inflation, the December 29, 1970 high of $842 would be equivalent to $842(160.5/38.8) =
$3483 in 1997. Therefore, the increase from $842 to $7801.63 represents a 124% increase, after adjusting
for inflation.
15.17
To determine trends and seasonal components, you need enough data for the patterns to become obvious.
Clearly, seasonal components require a number of repetitions of each season before they can be recognized.
If short series are examined, parts of irregular cycles could easily be mistaken for trends in one direction or
the other.
15.18
a. There is a clear increasing trend, so that would most likely explain the data. There may be a small
seasonal component, because people are more likely to move at certain times of the year, but it would be
small compared to the obvious trend.
b. Predicted population = −301 + (8.25)(100) = −301 + 825 = 504 thousand people.
c. The prediction is based on trends from 1950 to 1990. The prediction for the year 2000 may not be
accurate and the further into the future we try to predict, the less the trend is likely to hold. As the figure
below shows, the trend looks curved, not straight. Therefore, the prediction is likely to be too low.
d. The prediction was too low; the prediction was 504,000 and there were 656,600. It is obvious from the
plot in part c what went wrong. The prediction was based on a linear trend, and the trend was not linear.
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CHAPTER 15 SOLUTIONS AND MINI-PROJECT NOTES
NOTES ABOUT MINI-PROJECTS FOR CHAPTER 15
Mini-Project 15.1
Make sure the time periods are equally spaced on the plot. Clearly there won't be a seasonal component per se, but
there might be an analogous daily component, with slower pulse upon awakening and faster pulse at certain times of
the day. That's probably one of the lessons to be learned from the exercise. There isn't likely to be a trend. There
should certainly be random fluctuations.
Mini-Project 15.2
The four components should be mentioned. If the plot has been seasonally adjusted, that should be described as
well. If it has not, but should have been, the project should describe that fact.
Mini-Project 15.3
Most stock price indexes are not adjusted for inflation or seasonally adjusted. Adjustments for inflation can be done
using the CPI, but seasonal adjustments can't be done for this project. No matter what index is used, stock prices
traditionally have risen faster than inflation.
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