The graph illustrates the relationship between the number of sales and the number of employees is linear with the correlation coefficient of 0.922568. This means that there is a strong linear relationship between the number of sales and employees. 0,8511 or 85% (r²) of the variation in sales can be explained by a linear relationship with the number of employees. The remaining 15% can be explained with other factors such as economy, market influence, training and development approaches etc.
The regression analysis is:
0.2562 * number of employees + 0.0799 = number of sales.
This means, according to the regression analysis that for each additional thousand employees an extra £0.2562 billion or £256.2 million Euros would be earned. It is possible, but this also means that if thousand employees would be fired, the company would lose £256.2 million. So if using the number from the regression analysis data set, the number of sales would be predicted by the numbers of employees. But we must be careful, because if we compare two companies from the list and took for example Sudzacker and Cadbury Schweppes. Sudzacker’s sales are £5.8 billion and have 19.600 thousand employees. The sales of Cadbury Schweppes, on the other hand, are £3.4 billion and they have 23.500 employees.
From this example we see that a higher number of employees is not necessarily the factor of a higher sales. So, the validity of the prediction is limited and must be considered along with other factors.
The prediction must be caution. Even Nestle, according to the equation, earned more than they should. They should have earned £18.1 billion instead of 22.7 billion.
Part 2 - Value of retail sales from food stores
Data was collected from food stores in the UK about the value of retail (see appendix – part 2, figure 2.4) Figures are expressed in index numbers, with 2005 as a base year (2005=100). The sales were measured on a quarterly basis, starting from the 1st of 2003 until the 3rd quarter of 2009 (27 quarters).
In this graph (graph 1.2) we can see how the sales were evolved. Thus, we see that in every first quarter of the year, when it is winter, the sales are the lowest. In the second quarter, when it is spring, the sales go up. The third quarter the sales go a little down. Then the fourth and last quarter the sales go amazingly high comparing with the third quarter.
There is a high possibility that the December days are the cause. People buy more food during Christmas time and the holidays in December. Also the second quarter can be explained by the spring holidays.
An analysis of the sales data shows that the trend is linear. Centered moving averages and the trend line have been added to the original data, in order to indicate the evolution (graph 1.3). We can see that each year the whole sales have increased steadily, which can be seen also from ascendant orientation of the trend line in the graph. The trend is a straight line of the correlation. The determination r²=0.9773, which is very high. That indicates that 98% of the variation in the trend is in direct relation with the quarter number.
The regression equation is:
1.0884 * Quarter Number + 89.033 = Sales (index numbers)
Since each quarter increases by 1.0884, the average annual increase is 4.3536 index points.
As seen from the graphs, there are seasonal variations, and their averages are as follows:
On average, in the first three quarters of each year, the sales were under the trend, representing respectively 96%, 99% and 98% of the trend value, while in the fourth quarter the sales were above the trend, with 105% of the trend value.
Using the pattern observed along the years and the average seasonal variations, predictions can be made for the next quarters, for the 2009 and 2010 sales index:
As seen from the table, in the fourth quarter of 2009 food sales will increase by 26.4 index points comparing to 2005, and in the first three quarters of 2010 they will increase by 15.7, 21.6 and 20.3 index points comparing to 2005. The graph below (graph 1.4) illustrates these predictions, along with the original data. The predictions starting from quarter number 28.
These predictions were made supposing that the pattern will continue. This pattern is measured from 2003 to (with the predictions) 2010. Every single year the same numbers of sales are coming out. However, that does not mean that we can make predictions for a long term and count on them. There are some factors that could damage the prediction (such as economic crisis). Though, it is very handy to predict the next ten years if we are supposing that no external factors will come across.
Appendix
Part 1
Appendix
Part 2
