Effective Management Decision Making Language ... - Tutorsindia

Effective Management Decision MakingChapter 2(Remember y=bx+a as the general equation of a linear line (where a is the intercept on the y axis and b is the gradient of the line).By definition : (1) Σy = an +b ΣxAndΣxy=aΣx + bΣx 2 if multiplied through by ΣxIf a is substituted, you can derive:(2) b =( (nΣxy – ΣxΣy) / (nΣx 2 – ΣxΣx))And hence substituting this equation for b into (1) you can prove that (3) a= (Σy/n) – b(Σx/n) (or in other words that theintercept is the mean of the original y values less the mean of the x values multiplied by the gradient).So – if you wanted to work through a time series dataset to determine the appropriate equation for a best fit line, youcould simply use Excel and construct the following: Figure 2.7: Longhand construction of OLS calculationsValues for a and b have been determined by constructing the equations for them, in the cells of the excel worksheet (i.e.equations (2) and (3)). The figures in bold italic in the regression estimated sales column (on the right of figure 2.7) arethe true forecasts made only using the developed model of y=1.84x+28.73 (i.e. forecasts made when x=17,18,19 and 20).Clearly, once the cell formula have been set up and providing the assumptions which have been determined to underpinthe relationship between the dependent and independent variable – remain valid, you can ‘click and drag’ the finalforecasting column as far into the future (by increasing the x column) and the final forecasting column. A simple plot ofthis forecast and the original data shows the following:48Download free ebooks at bookboon.com