Concepts involving Business Analytics

Task One – Business Analytics Concepts

Part A

Cluster analysis is a method that groups the same observations into several clusters based on the observed values of numerous variables for every individual. Cluster analysis encompasses the organization of items into different groups based on how such groups or clusters are closely linked to one another. Cluster analysis aims to determine the same groups of subjects in that similarity between every pair of subjects implies some universal measure of the entire set of characteristics. Significantly, clustering analysis is characteristically utilized when no supposition is made about the probable associations within the data. The analysis provides insight regarding where relationships and patterns in the data are existent but does not provide information regarding what they may be or what they mean.

A fitting example of clustering analysis is classification. This encompasses the separation of the subjects into different groups so that every subject is more similar to other subjects contained in its groups compared to subjects that are not in that group. For instance, in the context of marketing, clustering analysis may be utilized to identify different categories within the consumer data, geographical location, age groups, earning levels, and even educational attainment. Similarly, in health care, clustering analysis may be beneficial in determining whether various geographical regions are associated with significant or insignificant levels of particular sicknesses to examine conceivable local contributing factors to health issues.

Part B

Cluster analysis is a categorization method for forming homogeneous groups contained in complex data sets. This section provides a critical discussion and analysis of five published papers that have capitalized on clustering analysis.

The article by Gaylord-Harden et al. (2008) used cluster analysis to implement the classification of adolescents based on their coping patterns and ascertain whether coping groups varied on fundamental correlates and coping outcomes such as stressors and psychological signs. In this study, the researchers utilized standard cluster analytic processes for categorizing adolescents into coping groups based on their coping behavior patterns concerning the study’s coping subscales. Initially, agglomerative hierarchical cluster analysis was carried out to determine the number of clusters within the sample. After that, k-means cluster analysis processes were utilized in grouping individuals. The research findings of cluster analysis pinpointed two comping groups that varied on the regularity of coping use and the preferred coping methods.

The article by Dollfus et al. (1996) sought to pinpoint subtypes of schizophrenia through cluster analyses. It is well-known that there are two subtypes of schizophrenia, including positive and negative. This study purposed to determine whether there are any possible further subtypes through the application of cluster analysis to a certain dataset. Specifically, the researchers applied Ward’s cluster analysis approach to scores of 138 patients based on the Positive and Negative Syndrome Scale (PANSS). Notably, research outcomes from the cluster analysis suggest four subtypes on the minimum including positive, negative, mixed, and disorganized. There was an additional subtype encompassing patients with minimal symptoms. These subtypes are deemed valid concerning the observed differences between the clusters on various clinical features and the likeness of the cluster solution attained from various instruments.

The research conducted by Ho and Hung (2008) employed cluster analysis to investigate how The authors employed Ward’s linkage clustering analysis. The study’s sample size comprised 640 potential students chosen from undergraduate programs in 14 different universities across the city of Taiwan. Specifically, cluster analysis was utilized to comprehend the causal dimensions of students’ choices based on the school’s selection criteria and classify students into recognizable groups. The outcomes of clustering analysis recognized five student groups for market segmentation. They comprise the Prominence cluster, the Less aware cluster, the Pragmatic cluster, the Austerity cluster, and the Fastidious cluster.

The study by Borgen and Barnett (1987) examines the application of cluster analysis in conducting counseling psychology research. Cluster analysis is a categorization method for forming homogeneous groups within complex data sets. This study determined different steps in conducting cluster analysis. The first step is measuring proximity to pinpoint objects with the most similarity. The second step is choosing the ideal clustering method, for instance, between the hierarchical and non-hierarchical approaches. The last step encompasses assessing and generalizing the clusters.

Also, the study conducted by DiStefano and Kamphaus (2006) investigated to examine subtypes of child development. Specifically, the study sought to compare the cluster analysis approach and latent class cluster analysis in the formation of typologies. These two classification methods were used to pinpoint groups of child behavioral changes underlying a sample of children within elementary level between the ages of 6 and 11 years. Information relating to students’ behavior was provided by teachers ranging from 14 different subscales and was utilized as input for the analyses. Subsequently, an analysis of these processes and outcomes were compared. Research outcomes determined that the latent class cluster analysis comprises three classes signifying varying levels of children’s behavioral adjustment while the cluster analysis comprised seven different child behavior categories. This implies a significant magnitude of overlap, and every process offers distinctive information for classifying child behavior.

Task Two – Marketing Analytics

a. Use Excel to determine the estimated demand quadratic equation function and describe why the quadratic form is preferred

A quadratic function takes the form, y = ax2 + bx + c. The estimated demand quadratic equation function is y = -2.1444x + 1751.7. The quadratic form is the most preferred because it can be used in solving any quadratic equation, and by using the standard form, it is conceivable to plug in the numbers. Significantly, suppose it is conceivable to express an equation in the quadratic form. In that case, it becomes conceivable to solve such an equation through any of the techniques utilized in solving ordinary quadratic equations.

b. Use Excel Solver to find the optimal price which maximizes the company’s profit

By creating a scatter plot, it is possible to determine the demand curve formula to be used as the basis for our model in the Excel Solver:

In this case, the demand curve formula is: d = 762.72 – 0.4252* p

By making use of the Excel solver, it is determined that the optimal price which maximizes the company’s profit is £1,336.90

c. Determine the optimal demand

Demand is 194

d. Compute the optimal profit

The optimal profit is 88,762

e. Interpret the results

As initially indicated, the demand curve formula is: d = 762.72 – 0.4252* p

It was determined that p is £848

Therefore, substituting p, we obtain:

d = 762.72 – 0.4252* £1,336.90

demand is 194

The optimal profit is determined by computing the total revenue less the total cost.

In this case, the total revenue is: (194.27 * £1,336.90) = £259,719.56

The total cost is: (194.27 * £880) = £170,957.60

The optimal profit is

Then the optimal profit is: £88,762

f. If the supply cost of each sofa is 750 and then 1050, determine the optimal price and interpret the results appropriately

The cost is £750, and the optimal price is £1,050

In this case,

The total revenue would be: £1,050 × 194 = £203,700

On the other hand, the total cost would be: £750 × 194 = £145,500

The total profit is obtained by revenues minus costs = £203,700 - £145,500

Therefore, the total profit is £58,200

This implies that decreasing the cost of production and supply and decreasing the optimal price resultant lower optimal profit.

g. If the company has decided to set the price more than 1200 GBP, what will be the optimal price? Interpret the results

As initially indicated, the demand curve formula is: d = 762.72 – 0.4252* p

It was determined that p is £1,200

Therefore, substituting p, we obtain:

d = 762.72 – 0.4252* £1,200

demand is 252

The optimal profit is determined by computing the total revenue less the total cost.

In this case, the total revenue is: (252* £1,200) = £302,400

The total cost is: (252 * £880) = £221,760

Then the optimal profit is: £80,640

Task Three – Forecasting

a. Plot the data and describe the main features of the series

The graph above illustrates a plot between the revenue generated and the financial quarters for 2014 to 2020. One of the main features of the series perceptible from the graph is a trend, with increasing values in the time series. Also, the trend appears to be exponentially increasing. Secondly, the variable shows seasonality as there is a repeating cycle over financial quarters in the time series. It is observable that the seasonal pattern is existent as the time series are impacted by seasonal factors, which is every third financial quarter of the year between 2014 and 2020.

b. Compute the four-period moving average and enter your values in the appropriate columns. Calculate the Centered Moving Average (CMA)/Baseline. Interpret it.

A moving average is used to obtain a general idea regarding trends within a data set. It is an average of any subsection or subgroup of numbers and is significantly beneficial in forecasting long-term trends. The chart below illustrates a 4-point moving average of the revenue generated in the 28 financial quarters in the seven years between 2014 and 2020.

Year

Q

Periods

Revenue

4-point Moving Average

Baseline/Centered Moving Average

2014

1

1

370

2014

2

2

585

602.5875

2014

3

3

930

615.4125

2014

4

4

493.7

594.675

631.425

2015

1

5

433.3

610.5

644.5875

2015

2

6

624.3

620.325

648.6875

2015

3

7

1018.8

642.525

653.725

2015

4

8

510.2

646.65

660

2016

1

9

449.6

650.725

665.6125

2016

2

10

648.3

656.725

670.75

2016

3

11

1045

663.275

678.2375

2016

4

12

528.9

667.95

692.4

2017

1

13

472

673.55

707.8625

2017

2

14

685.8

682.925

719.475

2017

3

15

1120.8

701.875

734.2

2017

4

16

576.8

713.85

758.75

2018

1

17

517

725.1

780.8375

2018

2

18

758.6

743.3

792.7125

2018

3

19

1244.4

774.2

804.3875

2018

4

20

629.9

787.475

819.15

2019

1

21

558.9

797.95

831.675

2019

2

22

810.1

810.825

839.5125

2019

3

23

1311

827.475

848.325

2019

4

24

663.5

835.875

861.625

2020

1

25

588

843.15

872.8125

2020

2

26

851.5

853.5

2020

3

27

1376

869.75

2020

4

28

688

875.875

The chart above demonstrates the baseline. Also referred to as the centered moving average, this alludes to the series that remains after the seasonality and the irregular constituents having been smoothed out through moving averages.

c. Calculate the Trend and interpret the trend.

The linear trend curve is y = 13.169x + 540.81

As is known, the linear curve is y =ax +b

In this case, a is 13.269, x is determined by the number of financial quarters, and b is a constant and is 540.81

d. Determine the Seasonality (St) and interpret it properly

Seasonality shows that similar revenues are perceived in every third fiscal quarter with an increment every consecutive financial year.

e. Forecast the revenue for the 8th year

The revenue for the 8the year can be forecasted using the linear equation that was obtained:

y = 13.169x + 540.81

It is imperative to note that in year 8, the financial quarters will be 29, 30, 31, and 32