REGRESSION LINE AND CORRELATION COEFFICIENT

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 :

rk = 1  –    6 ∑ D2

n(n2 -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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