[SOLVED] STA60104 QUANTITATIVE METHODS FOR BUSINESSHaskell

QUANTITATIVE METHODS FOR BUSINESS

STA60104

GROUP ASSIGNMENT

SEPTEMBER 2024 SEMESTER

Instructions:

1.   This assignment requires students to work in a group of 3 members. All members must come from the same tutorial group.

2.   You are required to submit a soft copy of your assignment report in Portable Document Format (PDF) in myTIMeS (Taylor’s Integrated Moodle e-Learning System) by 1 December 2024 (only one submission is allowed for each group). The assignment must be submitted to turnitin for the purpose of checking for any indications of plagiarism.

Question 1                                                                                                                 (17 marks)

A store manager would like to increase the number of items purchased by each customer. Currently, the probability distribution of the number of items purchased by each customer is given as follows:

Number of items purchased	0	1	2	3	4	5
Probability	0.05	0.10	0.20	0.40	0.15	0.10

The store manager is considering two options: He can offer more discounts to customers who purchased more items (Option 1) or he can reconfigure the layout of his store (Option 2). The respective revised probability distribution for the two options is given as follows:

Number of items purchased	0	1	2	3	4	5
Probability (Option 1)	0.05	0.05	0.10	0.20	0.30	0.30
Probability (Option 2)	0.05	0.05	0.15	0.20	0.35	0.20

(a)       Discuss whether the two options are able to increase the number of items purchased by each customer.           (6 marks)

(b)       Determine and justify which option is more effective in increasing the number of items that are purchased by each customer.          (2 marks)

(c)       Discuss whether the two options increase the variability in the number of sales.   (9 marks)

Question 2                                                                                                                (13 marks)

The government of a certain country is designing a subsidy policy based on the income of its citizens. Suppose the income of its country’s citizens is normally distributed with a mean of RM5000 and a standard deviation of RM1000.

The government is planning to design a subsidy policy whereby the country’s citizens are separated into three groups according to the citizens income, where Group I consists of citizens with the lowest 30% of income, Group II consists of citizens with incomes between Groups I and III, whereas Group III consists of citizens with the highest 20% of income.

The following table shows the amount of subsidy per year for the three groups.

Group	Subsidy per year
I	6000
II	3000
III	0

(a)       Determine the approximate range of incomes for each of the three groups.   (8 marks)

(b)       Evaluate the mean and standard deviation of the amount of subsidy per year.   (5 marks)

Question 3                                                                                                                (19 marks)

(Note: This question should be attempted using Excel)

An owner of two retail outlets would like to compare the monthly revenue of these two outlets. The following table shows the monthly revenue of these outlets for the past 4 years.

Month	Outlet A	Outlet B
1	39227	31777
2	36835	47369
3	40327	16864
4	33974	34079
5	48726	45257
6	45911	13191
7	38482	39313
8	42162	40169
9	36062	21097
10	40803	12851
11	38622	13228
12	36434	20587
13	38339	25075
14	39757	14239
15	40821	35287
16	43374	30809
17	37555	8821
18	39686	25762
19	37891	28634
20	40131	23539
21	44105	41088
22	43908	49523
23	30691	19432
24	47801	38125
25	45246	45411
26	45886	14012
27	48203	16824
28	39413	19058
29	44429	13659
30	41461	17680

(a)         Identify the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3) and the maximum for the monthly revenue for Outlets A and B. Use the function QUARTILE.EXC in Excel to find Q1, Q2  and Q3.                                         (5 marks)

(b)         Compute the lower and upper outlier limits for the revenue of Outlets A and B. Hence, determine whether there are any outliers.                                           (4 marks)

(c)         Based on parts (a) and (b), produce the box and whisker plots for the revenue of Outlets A and B. Subsequently, compare the two box and whisker plots in terms of the median, spread and shape.                                      (5 marks)

(d)         From the box and whisker plots in part (c), is it reasonable to conclude that Outlet A typically shows higher monthly revenue than Outlet B? Explain your answers.    (2 marks)

(e)         The owner speculates that the revenue for Outlet A correlates with the revenue for Outlet B. Discuss whether his speculation is valid.                                       (3 marks)

Watch the following videos for the guidelines to construct a box and whisker plot:

(i)       https://www.youtube.com/watch?v=39lsUsJsc2c

(ii)       https://www.youtube.com/watch?v=mhaGAaL6Abw

Question 4                                                                                                                (21 marks)

A retail company with 45 outlets is collecting data on possible variables that might have an impact on the weekly sales of each of its outlets. The attached Excel file contains data on the weekly sales of each of its outlets, together with the corresponding average temperature, fuel price, consumer price index (CPI) and unemployment rate for that particular week.

By selecting one of the stores (i.e. any store from  Store  1  to 45), answer the following questions. Attach the Excel output together with your solutions.

(a)         By selecting one of the variables (Temperature, Fuel Price, CPI or Unemployment Rate) as the independent variable, and Weekly Sales as the dependent variable,

(i)        form.  an estimated simple linear regression equation between the  selected independent variable and the dependent variable. Subsequently, interpret the slope coefficient of the equation.                                                       (2 marks)

(ii)       determine  and  interpret  the  correlation  coefficient  and the  coefficient  of determination.          (3 marks)

(iii)      at the 5% significance level, determine whether the data provide sufficient evidence that there is a positive or negative correlation between the selected independent variable and the dependent variable.              (2 marks)

(b)         By  selecting  all the variables  (Temperature, Fuel Price, CPI and Unemployment Rate) as the independent variables, and Weekly Sales as the dependent variable,

(i)     form an estimated multiple regression equation between the independent and dependent variables.  Subsequently,  interpret  the slope coefficients of the equation.                                                                                             (3 marks)

(ii)    determine  and  interpret  the  coefficient  of  determination  of the  multiple regression model.                    (1 mark)

(iii)   at the  1% significance level, use the critical value approach to test whether the overall multiple regression model is significant.                          (3 marks)

(iv)   at the 5% significant level, identify the independent variables that have a significant effect on Weekly Sales. Justify your answer.                   (4 marks)

(v)    construct scatter plots for the significant independent variables identified in part (iv) against the variable Weekly Sales. Comment on the scatter plots.   (3 marks)

To run regression analysis, you need to install the Data Analysis ToolPak in Microsoft Excel, watch the following video on the guidelines to install Data Analysis ToolPak in Microsoft Excel:

Watch the following videos for question 4(b) on multiple regression analysis:

•        https://www.youtube.com/watch?v=5nccswDrCUs&list=PLR- lkPxLxukAQ8HFkp10s_jXSfrj0YE8l&index=2

•        https://www.youtube.com/watch?v=EfxvaFvVPFU&list=PLR- lkPxLxukAQ8HFkp10s_jXSfrj0YE8l&index=4

•         https://www.youtube.com/watch?v=d_baG5cYKjg

•        https://www.youtube.com/watch?v=jGd2cj4K4Ww

•        https://www.youtube.com/watch?v=IQo_T7BmO90