MATH 2050 Application Project Due: Sunday, December 02, 2021, at 5:00 PM CT

MATH 2050 Application Project Due: Sunday, December 02, 2021, at 5:00 PM CT
This is a group project. Please create a group with a maximum of 5 students in each group and
send me an email that contains the Full Name of the group members by Monday, November
08, 2021. If you need any help, please let me know.
Advertising Dataset Description: The data set contains statistics about the sales of a
product in different markets together with advertising budgets in each of these markets for
different media channels: TV, Radio and Newspaper. The Sales are in thousands of units. The
budgets are in thousands of dollars.
Learning Outcomes:
1) Read the csv file using R
2) Perform the basic data preprocessing (manipulate and sort the variables, create the
data frame) using R
3) Create the basic data visualization using R and explain them in the context
4) Calculate the point estimate using R
5) Calculate the interval estimate using R
6) Interpret the results obtained to make a business decision
7) Internalize the concepts and make the connection to the real-world problems
How to turn it in?
Once you guys finish the work:
1) Please combine the work consisting of answers to all questions
2) Create a cover page with the name of all members of your group
3) Create a single pdf file that has first page as a cover page and the project report that
answers all the questions in a proper order.
4) Then each student will submit the assignment individually. The name of the file should
be your LastName_FirstName.pdf.
5) Please explain your work properly. The work that is unclear and without proper
explanation will lose many points. Please look at the following sample solution to the
problem 1.
For example, if you are in group 1, you work together with your group and combine your work
and create a single pdf file, then everyone submits the same pdf file (for problems 1 -10) to the
D2L dropbox folder for the Application Project but with the name of the file as your
LastName_FirstName.pdf.
For this project, please use the data set Advertising.csv data. I made the data available on the
D2L together with this project.
The details of the assignment of the project are as follows:
(1) [1 points]
i) Read the data Advertising.csv in R.
ii) Display the first six rows of the data. Write the name of the variables in the data.
ii) Display the name of the variables in the data. Explain your observation.
(2) [5 points]
i) Extract the variables sales, TV, radio, and newspapers from the data Adverting.csv. Give the
names sales, tv, radio, and newsp respectively.
ii) Create the data frame of tv, radio, newsp, and sales and name it All_sales.
(3) [5 points]
i) Create the data frame of the variables tv and sales.
ii) Create the side-by-side boxplot for these variables.
iii) Calculate the covariance and correlation coefficient between these variables. What can you
say from these values?
(4) [5 points]
i)Create the data frame of the variables radio and sales.
ii) Create the side-by-side boxplot for these variables. Explain your observation.
iii) Calculate the covariance and correlation coefficient between these variables. What can you
say from these values?
(5) [5 points]
i) Create the data frame of the variables newsp and sales and name it Newsp_Sales.
ii) Create the side-by-side boxplot for these variables. Explain your observation.
iii) Calculate the covariance and correlation coefficient between these variables. What can you
say from these values?
(6) [5 points]
i) In part (2) you created the data frame of all the variables tv, radio, newspaper, and sales and
name it All_Sales. Create the side-by-side boxplot for these variables. Explain your observation.
ii) Calculate the covariance and correlation coefficient between these variables.
iii) Create a pair plot using the function ggpairs from the R package GGally.
iv) Describe the observation you made from this visualization. Does this plot help you make a
business decision of where to spend money for advertising?
(7) [5 points]
i) Construct the density histogram for each of the variables tv, radio, newsp and sales.
ii) Describe the observations made from each of the histograms.
(8) [5 points]
i) Calculate the sample mean of all the variables in the data.
ii) Calculate the unbiased estimator of the true mean value of each of the variables.
ii) Calculate the sample standard deviation of all the variables in the data. What does these
numbers mean for this problem.
(9) [10 points]
i) State the Central Limit Theorem. Can we apply CLT to this data? Explain.
ii) Calculate the 95% confidence interval for the true average advertisement expenses on the
TV, based on the given sample data. Interpret the results.
iii) Calculate the 95% confidence interval for the true average advertisement expenses on the
newspaper, based on the given sample data. Interpret the results.
iv) Calculate the 95% confidence interval for the true average advertisement expenses on the
radio, based on the given sample data. Interpret the results.
v) Calculate the 95% confidence interval for the true average sales, based on the given sample
data. Interpret the results.
(10) [4 Points]
(i) Create an interesting as well as useful visualization and explain why is it useful? You can do
anything that makes sense to you.
(ii) Please explain your findings from the visualization.
Once you finished the problems from 1 through 10 and combine your work. Please answer the
question 11 individually at the end of the combined project work.
(11) [Bonus]
(a) Please mention the single most important contribution that each member of the team made
in the project.
(b) Write a half page reflection addressing the following questions:
(i) Which aspect of the project do you found most interesting to you?
(ii) Which aspect of the project do you found most challenging to you?
(iii) What concepts you learned in this project is helpful to you? Is this project help you clarify
the theory you learned during the class?
(iv) How may you use it in future to achieve your goal?
Rubric:
The assignment looks at the following components:
Connection to Experience (connects relevant experience and academic Knowledge)
Transfer (adapts and applies skills, abilities, theories, or methodologies gained in one situation
to new situations)
Integrated Communication (Makes Strategic and meaningful communication choices across
multiple contexts and purposes)
Reflection and Self- Assessment (Demonstrates a developing sense of self as a learner, building
on prior experiences to respond to new and challenging contexts (may be evident in self‐
assessment, reflective, or creative work.)