Linear Regression:
It means "dependence" and involves estimating the value of a dependent variable Y from an independent variable X. In simple regression just one independent variable is used whereas in multiple regressions two or more independent variables are involved. A simple linear regression model takes the form
Y = a + b X
where Y is the dependent and X the independent variable. A multiple linear regression equation can be of the form
Y = a + bX1 + c X2 + dX3.
A curvilinear relationship involving second-or higher-order functions can take the form
Y = a + bX + cX2 + dX 3
Simple linear regression is frequently satisfactory for forecasting purposes and in this unit we shall cover only linear regression and advise you to refer to any standard text on statistics for multiple regression and curvilinear regression models.
The forecasting process using regression is simple. The relevant data are obtained and plotted. Alternatively, an appropriate form of a model is selected. A trend equation is then developed, and utilized for forecasting. For the linear model
Y = a+ bX the slope b and the intercept a are determined as
b = ∑ XY - n X¯ Y¯ / ∑ X 2 - nX¯ 2
a = Y¯ - b X¯
Where X¯ = 1/ n (∑ X ); Y¯ = 1/ n (∑Y ); n is the number of pairs of observations made.
The regression line developed has the characteristics of a line of "best fit" meaning that the total of the squares of the vertical deviations from this line is less than the total of the squares of the deviations from any other straight line through the same points.