relationship between hospital cost and number of days in hospital. If the costs
are $100 for admission and $150 per day, we can easily calculate the total cost
given the number of days in hospital, and if any set of data is plotted, say cost
versus number of days, all data points fall perfectly on a straight line. Unlike a
deterministic relationship, astatistical relationshipis not perfect. In general, the
points do not fall perfectly on any line or curve.
Table 2.12 gives the values for the birth weight (x) and the increase in weight
between days 70 and 100 of life, expressed as a percentage of the birth weight
(y) for 12 infants. If we let each pair of numbersðx;yÞbe represented by a dot
in a diagram with thex’s on the horizontal axis, we have Figure 2.13. The dots
do not fall perfectly on a straight line, but rather, scatter around a line, very
typical for statistical relationships. Because of this scattering of dots, the dia-
gram is called ascatter diagram. The positions of the dots provide some infor-
mation about the direction as well as the strength of the association under the
investigation. If they tend to go from lower left to upper right, we have a posi-
tive association; if they tend to go from upper left to lower right, we have a
negative association. The relationship becomes weaker and weaker as the dis-
TABLE 2.12
x(oz) y(%) x(oz) y(%)
112 63 81 120
111 66 84 114
107 72 118 42
119 52 106 72
92 75 103 90
80 118 94 91Figure 2.13 Scatter diagram for birth-weight data.84 DESCRIPTIVE METHODS FOR CONTINUOUS DATA