Scatter Charts

The first step in the analysis is to plot each pair of values on a scatter chart.  At this stage it does not matter which variable is plotted on the horizontal (x) axis and which on the vertical (y) axis.

Suppose a personnel manager wanted to find out if employees who lived furthest away from work were late more than those who lived nearer. She would need to collect data from all employees on the distance travelled to work and on the number of times they have been late (say in the past three months).  In the following example, data is collected from the seven individuals concerned although it is preferable to have a larger sample.

Table 5.1

Employee	Distance from Work (km)	Number of Days Late (in 3 month period)
A. Teleka	15	6
J. Mhagama	5	3
D. Thengolose	20	4
M. Matekenya	2	0
W. Maruwo	3	1
Chimpesa	4	2
M. Sambani	10	4

Figure 5.1: Scatter Chart of Days Late Against Distance Travelled to Work

The chart shows that there is a tendency for those who live further away to be late more often.  The points lie reasonably close to a straight line with a positive gradient.

In another situation, an investigation of the relationship between length of service (in years) and annual salary gave the chart below.

Figure 5.2  Scatter Chart of Salary Against Length of Service

In this case there is no clear association between the length of service of an employee and the salary.  We say that there is no correlation between the two factors.

In a further example, we might want to look at the association between productivity, as measured by the unit cost, and volume of sales. This could be within a service organisation, e.g. for a hotel, the number of rooms sold and the hours paid.

Looking at the raw data (see Table 5.2) it is hard to see much of a pattern, though we might notice the highest costs occur when the volume of business is lowest.

Table 5.2 Relationship Between Volume of Business and Unit Cost

Time Period	Volume Business	Unit Cost (MWK)
1	2465	7.93
2	2699	7.33
3	2389	7.75
4	2408	7.55
5	2811	6.60
6	2209	8.40
7	2982	5.98
8	2802	6.87
9	2966	6.48
10	3182	5.94
11	2356	8.26
12	3262	5.87
13	2865	6.63
14	2484	7.36
15	2133	9.02

Figure 5.3: Relationship Between Volume and Unit Cost

We can now see that there is a clear negative relationship, i.e. low unit costs are associated with high volumes of business.  The points lie reasonably close to a straight line sloping downwards – a negative gradient.