Statistics >> Scatter Diagram
This is the simplest way of representing bivariate data. When data relating to the simultaneous measurement on two variables are available, each pair of observations can be graphically represented by a dot on a graph. Suppose (xi, yi); i = 1,2, ... , n be n pairs of values of the variables X and Y. Taking X on the horizontal axis and Y along vertical axis we get a diagram or n dots. This is called scatter diagram. If these points show some trend, the two variables are correlated and if the points do not reflect any trend the two variables have no correlation. If the trend of the points is upward rising, correlation is positive and if the trend is downward from left top to right bottom, correlations is negative. If the dots lie exactly on an upward rising straight line, then two variables are said to be perfectly positively correlated. Similarly, when all the dots lie exactly on a downward sloping straight line, then two variables are said to be perfect negatively correlated.
When the variation in the values of two variables are in a constant ratio, correlation is said to be linear. On the other hard, if the two variables are such that the amount of change in one variable does not result a constant ratio to the amount of change in the other variable, then correlation would be non-linear or curvilinear. In the first case a straight line y = a + bx would be obtained if all the points are plotted and in the second case we would not get a straight line.
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