Descriptive statistics
Figure 1: Rio’s sales volume (1998-2018) b Visual analysis
The sales volume of Rio displays a consistent upward trend, without noticeable cycles, but exhibits seasonal fluctuations, peaking in December and dipping in August and September each year This annual pattern is evident, with a significant irregular spike in 2008 due to the Whooping Cow disease, leading to an unusually high sales volume that year before returning to a steady increase from 2009 onwards.
Table 1: Descriptive statistics of Rio’s sales volume
The average sales volume over the analyzed period is 11.0495 tonnes, closely aligning with the median, while the maximum and minimum sales volumes recorded are 13.23 tonnes and 9.47 tonnes, respectively, signifying a narrow range in sales figures Notably, in 2008, the sales volume peaked at 13 tonnes due to a Cow disease outbreak that reduced the demand for dairy products, subsequently boosting the demand for Rio chocolate, which is not dairy-based The small standard deviation of 0.736 tonnes further highlights the limited variance in sales volume during this timeframe.
Model Analysis
Table 2: SPSS output (linear trend)
Table 3: SPSS model summary (linear trend)
As shown in Table 2, the estimated regression of linear trend is
To create quadratic trend, another variable, which is t^2, must be created Using SPSS, the following result is obtained
Table 4: SPSS output (quadratic trend)
Table 5: SPSS model summary (quadratic trend)
Based on Table 4, the estimated regression model is
To determine exponential trend, the dependent variable should be log (Yt) instead of Yt
Therefore, new variable, log (Yt) is created Using SPSS, we obtain the following regression result
Table 6: SPSS output (exponential trend)
Table 7: SPSS model summary (exponential trend)
Hence, the estimated regression is log (Yt)^ = 2.318 + 0.001*t
Among the three models analyzed, the linear trend regression is the most effective for illustrating changes in total sales volume over time, as evidenced by the line graph presented in Figure 1 and the visual analysis conducted in Part.
The analysis indicates a consistent upward trend in sales volume, suggesting that it increases at a steady rate over time Additionally, hypothesis testing on the coefficient of 't' in the linear regression model Yt^ + B1*t further supports this finding, confirming the significance of the trend in sales data.
H0: B1=0 (there is no linear trend)
The analysis presented in Table 2 reveals a p-value of 0.000, which is significantly lower than the 0.05 threshold Consequently, we reject the null hypothesis (H0) and conclude that there is a linear trend in the sales volume of Rio chocolate, with a confidence level of 95%.
The quadratic and exponential models are not appropriate for this data, as the quadratic model suggests a diminishing rate of increase followed by a downward trend, which is not reflected in the constant rate of change observed in Figure 1 Similarly, the exponential model indicates an increasing rate of change over time, a characteristic that is also absent in the data Consequently, the linear trend model emerges as the most fitting representation of the case.
Using excel, we obtain the SI as shown below
Table 8: Excel calculation of SI values
Figure 2: SI value in 12 months
Now we will incorporate the SI element into our regression model The below table is the SPSS output after we include SI.
Table 9: SPSS output for model with SI
Based on Table 9, estimated regression model is Yt^= -0.647 + 0.007*t + 0.108*SI
To determine whether SI has an impact upon sales volume, a hypothesis test is done upon B2 (the coefficient of SI)
H0: B2=0 (there is no seasonality effect on sales volume)
H1: B2≠0 (there is seasonality effect on sales volume)
According to Table 9, the p-value for B2 is 0.000, which is below the 0.05 significance level, leading us to reject the null hypothesis (H0) Therefore, we can confidently conclude, at a 95% confidence level, that seasonality significantly affects sales volume Additionally, the impact of disease on the sales of Rio chocolate is noteworthy.
Table 10: SPSS output of model with Disease dummy variable
Based on Table 10, estimated model is Yt^= -0.696 + 0.007*t + 0.108*SI +
1.037*D Hypothesis testing upon B3 (coefficient of disease)
H0: B3=0 (disease has no impact on Rio sales volume)
H1: B3≠0 (disease has an impact on Rio sales volume)
The p-value for B3 is 0.000, indicating a significant relationship between disease and Rio sales volume, as it is below the 0.05 threshold Consequently, we reject the null hypothesis (H0) at a 95% confidence level, confirming that the Disease dummy variable is significant Additionally, the coefficient value of B3, which is 1.037, suggests a positive correlation between disease presence and Rio sales volume.
Table 11: SPSS output of model including competitors’ prices
In Table 11, Pt represents the price of Rio chocolate while Pt_c1,2,3,…,8 represent price of CS, Gummi, Smartey, Heaven, Milkey, Treat, Lovely and Roca respectively.
Based on Table 11, our regression model is
Yt^= -0.864 + 0.007*t + 0.102*SI + 1.043*D – 0.242*Pt + 0.150*Pt_c1 + 0.262*Pt_c2 – 0.023*Pt_c3 + 0.039*Pt_c4 + 0.054*Pt_c5 + 0.035*Pt_c6 + 0.026*Pt_c7 – 0.029*Pt_c8
The definition of variables is summarised in the table below,
Types of variable Symbols Coefficient Definition
Dependent variable Yt Sales volume of Rio chocolate (in tonnes) Independent variables t B1 Time in months (t=1 represent Jan 98)
D B3 Presence of disease (1: disease presence, 0: otherwise)
Pt B4 Price per 100g ($) of Rio chocolate
The prices per 100g for various chocolate types are as follows: Caramel Squared chocolate, Gummi chocolate, Smartey chocolate, Heaven chocolate, Milkey chocolate, Treat chocolate, Lovely chocolate, and Roca chocolate Each chocolate offers a unique taste experience, catering to different preferences and budgets.
Table 11 indicates a negative correlation between Rio's price and its sales volume, as well as a similar negative relationship between the prices of Smartey/Roca and Rio's sales volume In contrast, other competitors show a positive correlation between their prices and Rio's sales volume Next, we will perform hypothesis testing to determine the significance of these variables.
The p-value of 0.00, as shown in Table 11, is below the significance level of 0.05, leading us to reject the null hypothesis (H0) This indicates, with 95% confidence, that a relationship exists between t and Rio sales volume, confirming a linear trend Consequently, t is identified as a significant variable.
H0: B2=0 (no seasonality effect on Rio sales volume)
H1: B2≠0 (there is seasonality effect on Rio sales volume)
The p-value of 0.000, which is below the 0.05 significance level, leads us to reject the null hypothesis (H0) and confirms, with 95% confidence, that there is a seasonal effect on Rio sales Consequently, seasonality is identified as a significant variable.
H0: B3=0 (no relationship between disease and Rio sales volume)
H1: B3≠0 (there is a relationship between disease and Rio sales volume)
The p-value of 0.000, which is below the 0.05 significance level, leads us to reject the null hypothesis (H0) This indicates, with 95% confidence, that there is a significant relationship between Disease and Rio sales volume, confirming that Disease is a significant variable.
H0: B4=0 (price of Rio chocolate has no effect upon its sales volume)
H1: B4≠0 (there is a relationship between Rio price and its sales volume)
The p-value of 0.001, as shown in Table 11, is below the significance level of 0.05, leading us to reject the null hypothesis (H0) This indicates a significant relationship between the price of Rio chocolate and its sales volume, confirming that price (Pt) is a crucial variable at a 95% confidence level.
H0: B5=0 (no relationship between caramel squared price and Rio sales volume)
H1: B5≠0 (there is relationship between caramel squared price and Rio sales volume)
The p-value of 0.037 indicates a statistically significant relationship between the price of Caramel squared chocolate and Rio sales volume, as it is below the 0.05 threshold Consequently, we reject the null hypothesis (H0) and assert with 95% confidence that Pt_c1 is a significant variable influencing sales.
H0: B6=0 (no relationship between price of Gummi chocolate and Rio sales volume)
H1: B6≠0 (there is relationship between price of Gummi chocolate and Rio sales volume)
The p-value of 0.000, which is lower than the significance level of 0.05, leads us to reject the null hypothesis (H0) This indicates a significant relationship between the price of Gummi chocolate and Rio sales volume at a 95% confidence level, confirming that Pt_c2 is a significant variable.
Let i denotes the chocolate brands number (Smartey:7, Heaven:8, Milkey:9, Treat:10, Lovely:11, Roca:12) and Bi denotes coefficient (i=7,8,9,10,11,12)
H0: Bi=0 (no relationship between price of brand i chocolate and Rio sales volume)
H1: Bi≠0 (there is relationship between price of brand i chocolate and Rio sales volume)
According to the analysis presented in Table 11, all p-values exceed the 0.05 significance level, leading to the conclusion that we do not reject the null hypothesis (H0) This indicates that, at a 95% confidence level, there is no significant relationship between the price of brand i chocolate and Rio sales volume Consequently, the variables Pt_c3,4,5,6,7,8 are deemed insignificant when evaluated individually.
Conclusion
Over the past 20 years, Rio chocolate has seen a significant increase in sales volume, with notable spikes in April, November, and December, when sales exceed the average (SI>100) This trend is largely attributed to seasonal events, as chocolate consumption rises during Easter in April and peaks during the Christmas season in November and December (Tannenbaum 2012; Johnson 2007) Conversely, sales dip in August due to the hot weather, leading consumers to prefer ice cream over chocolate (Smillie 2011) Thus, holiday periods drive higher chocolate sales, while summer heat contributes to lower sales in August.
In 2008, the outbreak of mad cow disease significantly impacted chocolate sales, leading consumers to avoid dairy products Brands like Rio, Caramel Square, and Gummi, which offer non-dairy chocolate, experienced a surge in sales as people switched to these alternatives Conversely, chocolate brands such as Smartey, Heaven, Milkey, Treat, Lovely, and Roca, which contain varying levels of milk, saw a decline in sales due to the health concerns associated with dairy consumption The data indicates that the greater the milk content in a chocolate brand, the more substantial the drop in sales during this period.
In 2008, sales volumes for Heaven and Milkey decreased by 25%, from approximately 8 tonnes to 6 tonnes, while Smartey's sales fell by 33%, from 9 tonnes to 6 tonnes Brands with higher milk content experienced even steeper declines, with Treat, Lovely, and Roca witnessing sales drops exceeding 50% This significant reduction highlights the impact of milk content on consumer preferences during that period.
In Part 2, we established a significant positive correlation between 't' and the sales volume of Rio, confirming an upward linear trend in sales This finding aligns with our visual analysis from Part 1 Additionally, our econometric analysis highlights seasonality as a crucial factor impacting Rio's sales volume.
Analysis of monthly sales data reveals that certain months, specifically April, November, and December, consistently exhibit higher sales figures each year, corroborating our earlier graphical observations Additionally, a significant positive correlation has been identified between disease occurrences and Rio sales volume, confirming that increased disease prevalence leads to heightened sales This correlation is particularly evident in 2008, when a spike in Rio sales coincided with an outbreak of Cow disease Overall, the econometric analysis aligns with the graphical data, reinforcing our findings.
The analysis reveals that higher prices for Rio lead to decreased sales volume, establishing a significant negative relationship between Rio's price and its sales Conversely, competitors' prices, specifically those of Caramel Squared and Gummi, positively influence Rio's sales, as these brands are considered direct competitors due to their similar non-dairy chocolate offerings An increase in the prices of Caramel Squared or Gummi is likely to divert customers to the relatively cheaper Rio, enhancing its sales volume In contrast, other brands that offer milk-based chocolates do not significantly impact Rio's sales, as they are not viewed as direct competitors.
To capitalize on the high demand for chocolate in December, Rio should consider building a substantial inventory in advance By negotiating significant deals with suppliers, Rio can secure lower material costs, leading to reduced unit production expenses This strategic approach not only prepares the company for increased sales but also enhances its profit margins.
This report analyzes external factors impacting Rio's sales volume, but to enhance sales, it is crucial for Rio to also consider internal aspects such as chocolate quality and variety Product quality remains the key to establishing a strong brand reputation and fostering customer loyalty Therefore, Rio should prioritize research and development to enhance product quality and introduce a wider range of offerings to meet diverse customer preferences, ultimately driving long-term sales growth.
Appendix
Appendix 1: Sales volume of Rio
Appendix 2: Sales volume of Caramel Squared
Appendix 3: Sales volume of Gummi
Appendix 4: Sales volume of Smartey
Appendix 5: Sales volume of Heaven
Appendix 6: Sales volume of Milkey
Appendix 7: Sales volume of Treat