Research Paper On Regression Analysis

3.4 STATISTICAL TOOLS

3.4.1 REGRESSION ANALYSIS

Regression analysis is a statistical process which helps to establish relationship between a dependent variable and one or more independent variables also known as predictors.The method may be parametric or non-parametric. The common ones are linear regression and ordinary least square regression.

REGRESSION MODELS

Regression model consists of three variables - the dependent variable denoted by Y, the independent variable denoted by X and an unknown parameter denoted by \beta . The regression model aims to explain Y as a function of X and \beta i.e E(Y|X)=f(X,\beta) .

UNDERLYING ASSUMPTIONS

The Regression analysis is based on certain assumption which are :-

• The sample should be

The quantity r, called the linear correlation coefficient, measures the strength and the direction of a linear relationship between two variables. The linear correlation coefficient is also referred to as the Pearson product moment correlation coefficient. The mathematical formula for computing r is:

r=\frac{n\sum xy-(\sum x)(\sum y)}{\sqrt{n(\sum x^{2})-(\sum x^{2}}\sqrt{n(\sum y^{2})-(\sum y)^{2}}}

where n is the number of pairs of data.

The value of r may be positive or negative signifying positive and negative linear correlations respectively. Exactly +1 and -1 value represents a perfect positive and negative perfect fit. The + and – signs are used for positive linear correlations and negative linear correlations, respectively. If r is close to 0, it is an indication of a random, nonlinear relationship between the two variables. r does not rely on the units employed and is a dimensionless quantity. When all the data points lie exactly on a straight point, a perfect correlation of ± 1 is noted. A perfect correlation of occurs only when the data points all lie exactly on a straight line. The slope of the line is positive if r = +1, and negative if r = -1. A rule of thumb is that a correlation less than 0.5 is a weak while a value greater than 0.8 is described as