Back to: Further Mathematics SS2

**SCATTER DIAGRAM**

**Definition:** a scatter diagram is a graphic display of bivariate data. A bivariate data involves two variables

**TYPES OF SCATTER DIAGRAM:**

**Linear positive correlation.**

A positive correlation between two variables x any y means that in general, increase in x is accompanied by increase in y. The regression line has a positive slope.

**Linear negative correlation**

A negative correlation between x and y means that an increase in x is accompanied by a decrease in y, negative correlation has a negative slope.

**REGRESSION LINE OR LINE OF BEST FIT OR THE LEAST SQUARES LINE**

There are two variables where one is dependent and the other is independent variable. The regression line can be fit using scatter diagram method and the least squares method.

** LEAST SQUARES METHOD**: If x is independent variable and y dependent variable, that is y on x. then :The equation of the regression line is written as y = ax + b

Where a is the slope and b is the y – intercept. Given two sets of variables x and y it can be deduced that

**CORRELATION COEFFICIENT**

*DEFINITION:*

The correlation coefficient determines the amount or degree of linear relationship between two variables. The correlation coefficient is represented by r

The characteristics of r are as follows:

1. The value of r is the same irrespective of the variable labelled x or y.

2. the value of r satisfies the inequality -1__<__ x __<__ + 1

3. if r is close to +1, the variables are highly positively correlated. If r is close to -1 then, x and y are highly negatively correlated. If r is close to zero, the correlation between x and y is very low. There is no correlation between x and y when r = 0

There are two methods of obtaining the correlation coefficient.

1. Pearson’s coefficient of correlation or product moment correlation coefficient

2. Rank correlation coefficient.

**RANK CORRELATION COEFFICIENT**: It is also known as Spearman’s rank correlation coefficient and defined as :

**r _{k} = 1 – 6 ∑ D^{2}**

**n(n ^{2} -1)**

As the name implies, the variables (if not ranked) can be ranked in ascending order or descending order. Where there are ties, the average is used as the rank.

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