STA60104 QUANTITATIVE METHODS FOR BUSINESS

Question 1 

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:

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:

(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.

Question 2-

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 their 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.

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

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

Question 3

(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.

(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.

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

(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.

(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.

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

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 

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/watchv=5nccswDrCUs&list=PLRlkPxLxukAQ8HFkp10s_jXSfrj0YE8l&index=2
•https://www.youtube.com/watchv=EfxvaFvVPFU&list=PLRlkPxLxukAQ8HFkp10s_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

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