Descriptive statistics
Figure 1: Rio’s sales volume (1998-2018) b Visual analysis
Based on Figure 1, the sales volume of Rio generally follows an upward trend There seems to be no cycle appearing in the trend However, it is clear that there is seasonality effect on the sales volume. Within a year, Rio sales volume is the highest towards the end of the year (around December), while the sales remain low in the middle of the year (around August and September) This pattern repeats every year Besides, there was an irregular fluctuation happening in 2008 when Whooping Cow disease took effect The sales volume of Rio in this year was much higher as compared to other periods Therefore, there was a certain spike in the sales volume in 2008 before it fell back and continued with the increasing trend from 2009 onwards c Descriptive statistics
Table 1: Descriptive statistics of Rio’s sales volume
According to Table 1, the mean sales volume is 11.0495 tonnes, which is quite closed to the median,while the maximum and minimum sales volumes are 13.23 tonnes and 9.47 tonnes respectively This indicates the small spread in sales volume In Figure 1, it is obvious that the sales volume of 13 tonnes happened in 2008 when there was a Cow disease This is closed to the maximum sales over the past 20 years Such a high sales volume in 2008 was due to Cow disease that created low demand for dairy products Since Rio is not made from milk, there was an increase in demand for Rio chocolate, making it sales higher Standard deviation is small (0.736 tonnes), which indicates that there is not much variance in the sales volume.
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
Out of the 3 models, linear trend is the most suitable regression to depict the change in total sales volume over time This is because based on the line graph (Figure 1) and the visual analysis in Part 1, there seems to be an upward linear trend in sales volume The dependent variable (sales volume) seems to increase at a constant rate Moreover, by conducting hypothesis testing upon the coefficient of ‘t’ in the linear regression model Yt^ + B1*t,
H0: B1=0 (there is no linear trend)
As shown in Table 2, the p-value is 0.000 which is less than 0.05 (significant level) Hence, we reject H0 and conclude that, at 95% confidence level, there is a linear trend in the sales volume of Rio chocolate
Besides, the quadratic and exponential trends are not likely to be fitted in this case because under quadratic model, there is an upward trend Yet the rate of increasing of the trend gets smaller over time After a maximum point, a downward trend follows Looking at Figure 1, the rate of change seems to be constant rather than diminishing Therefore, quadratic model can be omitted The same reasoning can be applied to exponential model as well Under exponential trend, the rate of change will increase over time Such a characteristic is not observed in Figure 1 Therefore, exponential model is not fitted As a result, the linear trend model is the most suitable depiction of the case This is our final regression model
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)
Based on Table 9, p-value of B2 is 0.000 which is less than 0.05 (significant level) Hence, we reject H0 and conclude, at 95% confidence level, that there is an effect of seasonality upon sales volume c) Impact of Disease on the sales of Rio chocolate
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 of B3 is 0.000 which is less than 0.05 (significant level) Hence, we reject H0 and conclude, at 95% confidence level, that there is a relationship between disease and Rio sales volume. Therefore, Disease dummy variable is a significant variable Based on the value of B3 (1.037), there is a positive relationship between Disease and Rio sales volume d) Impact of competitor’s pricing
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 ($) of Rio chocolate
Pt_c1 B5 Price per 100g ($) of Caramel Squared chocolate Pt_c2 B6 Price per 100g ($) of Gummi chocolate Pt_c3 B7 Price per 100g ($) of Smartey chocolate Pt_c4 B8 Price per 100g ($) of Heaven chocolate Pt_c5 B9 Price per 100g ($) of Milkey chocolate Pt_c6 B10 Price per 100g ($) of Treat chocolate Pt_c7 B11 Price per 100g ($) of Lovely chocolate Pt_c8 B12 Price per 100g ($) of Roca chocolate
Looking at the coefficients in Table 11, there seems to be a negative relationship between Rio price and its sales volume Similarly, there is a negative relationship between price of Smartey/Roca and Rio sales volume For the remaining competitors, there is a positive relationship between their price and Rio sales volume Now, we will conduct hypothesis testing to check significance of the variables. Hypothesis testing on B1, B2, B3, B4, B5 and B6
The p-value is 0.00 (Table 11) which is less than 0.05 (significant level) Hence, we reject H0 and conclude at 95% confidence level that there is a relationship between t and Rio sales volume (there is linear trend) Therefore, t is 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 is 0.000 (Table 11) which is less than 0.05 (significant level) Hence, we reject H0 and conclude at 95% confidence level that there is seasonality effect on Rio sales Therefore, SI is 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 is 0.000 (Table 11) which is less than 0.05 (significant level) Hence, we reject H0 and conclude at 95% confidence level that there is a relationship between Disease and Rio sales volume. Therefore, 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 is 0.001 (Table 11) which is less than 0.05 (significant level) Hence, we reject H0 and conclude at 95% confidence level that there is a relationship between price of Rio chocolate and its sales volume Therefore, Pt is a significant variable.
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 is 0.037 (Table 11) which is less than 0.05 (significant level) Hence, we reject H0 and conclude at 95% confidence level that there is a relationship between price of Caramel squared chocolate and Rio sales volume Therefore, Pt_c1 is a significant variable
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 is 0.000 (Table 11) which is less than 0.05 (significant level) Hence, we reject H0 and conclude at 95% confidence level that there is a relationship between price of Gummi chocolate andRio sales volume Therefore, 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)
Based on Table 11, p-values are all greater than 0.05 (significant level) Hence, we do not reject H0 and conclude that, at 95% confidence level, there is no relationship between price of brand i chocolate and Rio sales volume Therefore, variables Pt_c3,4,5,6,7,8 are all insignificant when tested individually
Before removing these variables from the model, we need to check whether these variables are jointly significant Hence, F-test is used in this case, the following tables depict unrestricted and restricted models using SPSS.
Table 13: Output of Unrestricted model (all variables included)
Table 14: Output of restricted model (Pt_c3,4,5,6,7,8 variables are restricted)
- H0: B7012=0 (Pt_c3,4,5,6,7,8 are not jointly significant)
- H1: at least one Bi ≠ 0 (i=7,8,9,10,11,12) (at least one out of Pt_c3,4,5,6,7,8 is significant under joint testing)
Based on SSR values found in Table 13 and 14,
Conclusion
Overall, there is an increasing trend in the sales volume of Rio chocolate over the past 20 years.Based on Table 8, out of 12 months, April, November and December are the 3 months with higher- than-average sales of chocolate (SI>100) while the other months experience lower-than-average sales (SI