# Simple Regression

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Simple regression is used when one wants to predict value of one variable given values of another variable or it is used to find the relationship between two variables. It is a method that can be used to determine the relationship between a continuous process out put (y) and one factor (x). The relationship can be expressed in the terms of a mathematical equation such as y= a+bx. where x and y are the variables and b the slope, a= to the intercept point of regression line and the y axis. The value b which is the slope is equal to ;

The slope (b) = (N∑XY – ( ∑X)( ∑Y))/((N∑ X^{2 }- (∑X)^{2 }) and

The intercept (a) = (∑ Y-b(∑X))/ N

N is the number of elements of the variables x and y where X and Yare the individual values of the different variables and the sign for summation of the values is ∑ where ∑XY sum of the product of the values of X and Y, and ∑X is the sum of the values of x and ∑Y is the sum of the values of y and ∑ X^{2 } the sum of the square of the values of x (Hiox calculator n.d).

Multiple Regression

Multiple regression is used where we want to predict the value of one variable from several independent variables. In multiple regression the several independent variables are used to predict the dependent variable we can use an equation such as the one sampled below.

Y= a+ b_{1}X_{1 }+ b_{2}X_{2 ….}. + b_{k}X_{k}.

Using the given formula Y is the value of the dependant variable or what is being predicted, whereas a is the constant or intercept. Variables that follow are independent and they should not be correlated. They are expressed as x_{1,} x_{2……}x_{k }. These are the several independent variables that will be used to forecast the dependant variable Y. The values of b_{1,} b_{2…. }b_{k }are coefficients which are equal to the slopes of the independent variables (StatSoft, 1998).

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