# Analytical and Statistical Methods

**Definition: **There are several **Analytical and Statistical methods** of sales forecasting, that a firm can employ on the basis of its forecasting needs. These methods are listed below:

**Simple Projection Method:**Under this method, the firm forecast the current year’s sales by simply adding up the expected growth rate to the last year’s sales. This growth rate can be determined by either considering the industry’s growth rate or by taking the growth rate achieved by the top company (leader) in the industry. Often the companies use the following formula to arrive at the sales projection:**Next year’s sales = (Current Year’s Sales)**^{2 }/ Last Year’s SalesThis method proves to be fruitful for only those firms whose sales are relatively stable or show an increasing trend.

**Extrapolation Method:**The extrapolation method is again a project/trend method, but is quite complex than the simple projection method. Here, the sales figures of past several years are plotted on graph paper and the points are connected via a line which is further stretched to obtain the future sales figures.It is assumed that the future sales will follow the same pattern as followed by the past sales trend and observes the same curve on a graph. This method can be applied effectively where the firms have the steady past sales and expect no abrupt disruptions in the future.

**Moving Averages Method:**The moving averages method is used to predict future sales more accurately by eliminating the effects of seasonality and other irregular trends in sales. This method provides the time series of moving averages.Here, each time series point is the arithmetical or the weighted average of a number of preceding consecutive points. Minimum two years past sales data are required in case the seasonal effects on the sales persists.

**Exponential Smoothing:**The exponential smoothing is yet another projection method and works on the similar guidelines of the moving averages methods. Here also, each point of time series is the arithmetical average of preceding consecutive points and where the heaviest weight is assigned to the most recent data.This method is often used in the situation where the data under forecast is large. The exponential smoothing has the stable response to change, and the response can be changed accordingly.

**Time Series Analysis:**The time series analysis is yet another most extensively used sales forecasting method wherein the sales of several continuous years are chronologically ordered, and the pattern is studied thereafter. The time series method helps in analyzing the following:**The Seasonal Variation**, i.e. the change in the sales due to the seasonal variations.**The Cyclical Patterns,**i.e. the sales pattern that repeat itself after every year.**Trends in Data****The Growth Rate,**i**.**e. the rate at which the sales grow with each year.This method is based on the assumption that the factors affecting the sales do not change much over a period of time and hence the future is derived from the past.

**Regression Analysis:**This method is adopted to study the functional relation of those factors that influence sales. The sale is the dependent variable while the factors that influences sales are explanatory or causal variables. Thus, in this method, the relationship between the dependent variable (sales forecast) and the causal variable is measured. The following regression equation shows the different relationships between the sales and the factors influencing the sales:**Y = a+b**_{1}x_{1}+b_{2}x_{2}+…..+b_{n}x_{n}**Where**, Y = sales,

x_{1,}x_{2 }…..x_{n }represents the causal factors

b_{1},b_{2}….b_{n }are the constants that show the extent to which the causal factors contribute towards the sales.

**Complex Econometric Models:**This is an another analytical method of sales forecasting wherein the economic theories are expressed in the mathematical terms so that these can be verified by the statistical methods. This method is used to predict the future events by measuring the impact of one economic variable upon another.

The econometric model depends on the following principles:- Sales of any product depend on several variables.
- The sale is the dependent variable while the casual factors are the independent variables.
- There is a constant interaction between the sales and the causal factors.
- Also, there is a constant interaction among the independent variables themselves.
- There are two types of independent variables:
**exogenous variables**(constitutes non-economic forces, such as nature, or politics) and**endogenous variables**(economic forces, such as income, price, employment, etc.) - The interrelationship between sales and the independent variables can be determined through the statistical analysis of the past data.

Thus, a company can use either of these methods to forecast the demand for goods and services and set the sales objectives accordingly.