Posted: April 13th, 2023

Journal Article (Mathematical Statistics) essay

Journal Article
Sample Data for Supermarket Profits
Supermarket Number Food Sales (tens
of thousands of dollars)
Nonfood Sales
(tens of thousands of dollars)
Store Size
(thousands of square feet)
Profit (thousands of dollars)
Y
1 305 35 35 20
2 129 98 20 15
3 189 83 27 17
4 175 76 16 9
5 101 93 28 16
6 269 77 46 27
7 425 44 58 35
8 195 47 12 7
9 282 31 40 22
10 203 92 32 23

You have to indicate the purpose of the study and discuss (not listing) data characteristics before answering questions and interpreting the results of the regression analysis.

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1. Run a multiple regression using the above data. (with profit as the dependent variable).
2. Compare the result of question (1) with another regression equation obtained without the food sales variable.
3. Which of the models do you prefer? Why?
4. Interpret your results for (1) and (2).
5. In writing your paper, you should start by indicating the purpose of the study. Also, discuss the methodology and conclusions.

** You can use EXCEL or any other software. ** You need to include your printout in your submissions.
The layout and format of the paper should include the following sections:
Title page, Abstract, Introduction, Method, Results, and Discussion.
a) Abstract is a very concise summary of the paper.
b) The Introduction tells the reader about the topic. Specifically, it should start with the purpose of this paper is to examine…. What the issue is, what is known about it, and the specific focus? Put a business context to it -- write the value added by your work or what businesses can gain from the knowledge of the determinants of market profits.
c) Empirical Results you should start with a brief discussion of the descriptive statistics for each variable.
d) Method you should be able to explain what method you are using for your work. For example, you can start with telling the reader that the ordinary least squares method (OLS) was used to obtain estimated coefficients... (Then write more). You should be able to write the equation from the Excel result. We expect to see you… 1. Using the excel result to generate the equation.
2. Find the standard error of each variable.
3. Find the t-stat of each variable.
4. Find the p-value of each variable.

EXAMPLE:
Ŷ = 1.24 + 1.71x1 - 0.83x2 - 2.12x3
(6.79) (1.43) (0.22) (0.85) T-stat [0.18] [1.20] [3.78] [2.48]
P-value 0.857 0.247 0.002 0.025

e) The results section should tell what was found from the computed data. Using Chapter 10 and 11 for helping you interpret your result. For instance, you should interpret the Coefficient of Determination (R!), F-test, t-test, p-value and etc. In addition, your result should use the hypothesis equation.
Remember that in the results section there should include hypothesis testing for a t-test about each slope coefficient and a F-test for the overall regression model.
EXAMPLE:
For the t-test, it is written like this:
H":
H$: β
Note:
You have to decide whether to use one-tail or two-tail test
You need to follow chapter 9 materials and declare your alternative hypothesis in each case very well

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F-test:
H":
H$: , or all three are
(Note that: remember to mention what α is used in your hypothesis testing).

f) The Discussion describes what your findings mean in the light of the information presented in the introduction. It is the interpretive segment of the paper and loops back to answer the issues raised in the introduction. Remember to answer questions 2 and 3.