MAT 114 QUANTITATIVE REASONING
SUMMER 2016
PROJECT TWO
The objective of this project is to use a spreadsheet program to test correlation strength and to create and
utilize mathematical functions which model relationships between pairs of quantities, especially relationships
which demonstrate linear or exponential growth/decay.
Additionally, a major component of this project is utilizing several important functions within standard
spreadsheet software, such as Microsoft Excel. Please note that developing proficiency with such software is
required for the successful completion of this project and may take considerable time and effort if you do not
already have extensive familiarity with such software.
Important definitions and helpful examples related to this project are provided in Chapter 3 of the NAU MAT
114 course website. Specifically:
3A – independent/dependent variables, positive/negative correlation, correlation coefficient
3B – comparing linear and exponential growth/decay
3E – implementing functions using Microsoft Excel (video example)
A spreadsheet file containing the data sets required for this project must be downloaded from the NAU MAT
114 course website.
All required charts/graphs must be created within a spreadsheet program. Handwritten or hand-drawn
charts/graphs will not be accepted.
Answers to the following questions must be compiled into a single word-processing document (Microsoft
Word, etc.), including necessary explanatory text and supporting charts/graphs. Explanations and discussions
of answers must be in complete, grammatically correct sentences. The final document must be neat and
organized, with answers to individual problems clearly labeled. The method of submission of the final
document (i.e. printed out, submitted electronically, etc.) will be determined by individual instructors.
This project must be submitted prior to the start of your Class Meeting during Week 10 of this semester.
MUTUAL FUNDS
As with any business, running a mutual fund involves costs. For example, there are costs incurred in
connection with particular investor transactions and there are also regular fund operating costs that are not
necessarily associated with any particular investor transaction.
1. Data in the accompanying spreadsheet documents the average annual operating expenses for a sample of
15 mutual funds. In addition, the average annual return for each mutual fund is given.
a) Does it appear these quantities are positively related or negatively related? Why, do you think, these
quantities would be related in this way?
b) Create a scatterplot of the data.
(This is accomplished in Microsoft Excel by highlighting all of the data, clicking the “Insert” tab,
and selecting “Scatter”.)
c) Have your spreadsheet program create a linear regression trendline for the data, displaying the
equation and the coefficient of determination (R2) on the graph.
(This is accomplished in Microsoft Excel by right-clicking on a data point in your scatterplot,
selecting “Add Trendline…”, and selecting “Display Equation on chart” and “Display R-squared
value on chart”.)
**Include a copy of this scatterplot in your report.
d) Find the correlation coefficient R for your linear regression trendline. Does that value indicate a strong
correlation or a weak correlation?
Note: You must calculate and discuss R, but the spreadsheet program displays R2.
e) Based on the linear regression trendline you just generated, what average annual return would you
expect from a mutual fund that had 1.7% average operating expenses? Please show calculations to support
your answer.
f) Based on the linear regression trendline you just generated, what average operating expenses would you
expect to pay for a mutual fund with an average annual return of 8%? Please show calculations to support
your answer.
g) Have your spreadsheet program create an exponential regression trendline for the data, displaying the
equation and the coefficient of determination (R2) on the graph. Find the exponential correlation
coefficient (R).
**Include a copy of this scatterplot in your report.
h) Based on the two correlation coefficients you have just calculated, which type of function (linear or
exponential) appears to be a better fit for this data?
PROTEIN BARS
The consumer services website findthebest.com has the goal of “collecting, structuring, and connecting all the
world’s data so you have everything you need to research with confidence.”
Data in the accompanying spreadsheet details nutritional information for 100 protein bars which were rated on
findthebest.com.
2. a) Create a scatterplot for each pair of quantities below. Have your spreadsheet program create a linear
regression trendline for each scatterplot, displaying the coefficient of determination (R2) on the graph.
Protein vs. Calories
Protein vs. Carbohydrates
Carbohydrates vs. Calories
**Include each of these scatterplots in your report.
b) Find the correlation coefficient R for each linear regression trendline you just generated.
c) Based on the correlation coefficients you just calculated, which pair of nutritional quantities appear to
have the strongest correlation? Would you categorize this correlation as very strong or only moderately
strong?
d) Based on the correlation coefficients you just calculated, which pair of nutritional quantities appear to
have the weakest correlation?
3. a) Create a column adjacent to the given table which calculates the Protein per Calories for each of the
protein bars listed.
b) What is the highest value for Protein per Calories attained by one of the protein bars listed? Include
units when stating this value.
c) Create a column adjacent to the given table which calculates the Protein per Carbohydrates for each of
the protein bars listed.
d) What is the highest value for Protein per Carbohydrates attained by one of the protein bars listed?
Include units when stating this value.
CIGARETTE TAXES
State and federal taxes on tobacco products began in the United States in 1794. The rate of such taxes over the
last roughly fifty years has varied significantly. The following problems will model the approximate number of
cigarettes consumed in the United States since 1960 along with the varying amount of taxation on a single pack
of cigarettes, leading to a projection of the total tax revenue generated by cigarette sales.
4. a) The number of packages of cigarettes consumed in the United States during the year 1960 was 484.4
billion. During the 1960’s, this number increased by roughly 1% per year. Create a table of values
indicating the number of packages of cigarettes consumed each year from 1960 to 1969.
b) During the 1970’s, the number of packages of cigarettes increased by roughly 1.65% each year. Continue
your table of values to indicate the number of packages of cigarettes consumed from 1970 to 1979.
c) During the 1980’s, cigarette use dropped in the U.S. at a roughly of roughly 1.8% per year. Continue
your table of values to indicate the number of packages of cigarettes consumed from 1980 to 1989.
d) Starting in 1990, the decline in cigarette use has been roughly 2.15% per year. Continue your table of
values to indicate the number of packages of cigarettes consumed from 1990 to 2014.
5. The combined state and federal excise tax charged on a package of cigarettes was $ 0.26 in 1960 and
increased by approximately $ 0.01 each year until 2008. Major federal legislation passed in 2009 caused
the tax charged on a package of cigarettes to increase by $ 0.62 over the tax charged in 2008. Since 2009,
primarily due to increased taxes charged by state governments, the overall tax charged on a package of
cigarettes has increased by roughly 12.9% each year. Create a column of values which indicates the tax
charged on a package of cigarettes from 1960 to 2014.
6. a) Create a column of values indicating the amount of tax revenue generated by cigarette sales each year
from 1960 to 2014.
b) Create a multi-line graph displaying the number of packages of cigarettes and the tax revenue generated
by taxes on cigarettes from 1960 to 2014.
**Include your completed table of values and your multi-line graph in your report.