**Understand and Learn, Explain to the Multiple-Regression Analysis! **

In the multi-regression analysis, the regression equation is used where demand for the commodity is deemed to be the functions of many variables. **Meaning of Multiple-Regression:** Multiple regression is a statistical tool used to derive the value of a criterion from several other independent, or predictor, variables. It is the simultaneous combination of multiple factors to assess how and to what extent they affect a certain outcome. **Also learn, Explain to the Multiple-Regression Analysis!**

**The process of multi-regression analysis may be briefly described as:**

- The first step in multiple regression analysis is to specify the variables that are supposed to explain the variations in demand for the product under reference. The explanatory variables are generally chosen from the determinants of demand, viz. price of the product, the price of its substitute, consumer’s income and their tastes and preference. For estimating the demand for durable consumer goods (e.g. TV sets refrigerators, houses etc,), the explanatory variables which are considered are the availability of credit and rate of interest. For estimating the demand of capital goods (e.g. machinery, and equipment) the relevant variables are additional corporate investments, the rate of depreciation, cost of capital goods cost of other inputs (e.g., labor and raw materials) market rate of interest etc.
- Once the explanatory or independent variable is specified, the second step is to collect time-series data on the independent variables.
- After necessary data is collected, the next step is to specify the form of the equation which can appropriately describe the nature and extent of the relationship between the dependent and the independent variables.
- The final step is to estimate the parameters in the chosen equations with the help of statistical techniques. The multivariate equation cannot be easily estimated manually. They have to be estimated with the help of computers.

The reliability of the demand forecast depends to a large extent on the form of equation and degree of consistency of the explanatory variables in the estimated demand function. The greater the degree of consistency, the higher the reliability of the estimated demand and vice versa. Adequate precautions should, therefore, be taken in specifying the equation to be estimated.

**The multiple linear regression equation is as follows:**

,

where is the predicted or expected value of the dependent variable, X_{1} through X_{p} are p distinct independent or predictor variables, b_{0} is the value of Y when all of the independent variables (X_{1} through X_{p}) are equal to zero, and b_{1} through b_{p} is the estimated regression coefficients? Each regression coefficient represents the change in Y relative to a one unit change in the respective independent variable. In the multiple regression situation, b_{1}, for example, is the change in Y relative to a one unit change in X_{1}, holding all other independent variables constant (i.e., when the remaining independent variables are held at the same value or are fixed). Again, statistical tests can be performed to assess whether each regression coefficient is significantly different from zero.

**Selection of the Forecasting Model: **We have discussed several statistical forecasting models for demand estimation in planning and control. As a manager, you now have the task of selecting the best model for your needs. Which one should you choose, and what criteria should you use to make the decision. The most important criteria are:

- cost, and
- accuracy

Accuracy (forecast error), can be converted into the cost. Costs to be considered in the model selection are:

- implementation costs,
- systemic costs,
- Forecast error costs.

Of these three, forecast error costs are perhaps the most complex to evaluate. They depend upon the noise in the time series, the demand pattern, the length of the forecast period and the measure of the forecast error. Several studies have evaluated and compared the performance of different models. In general, different models are best, depending on the demand pattern, noise levels and length of the forecast period. It is typical to have a choice of several good models for anyone demand pattern when the choice is based only on forecast error.** **

**Combining Naïve Forecasting Models: **In comprehensive studies, it has been found that average and weighted average methods of forecasting are different from other forecasting methods. From these studies, we can conclude that forecasting accuracy improves and that the variability of accuracy among different combinations decreases, a number of methods in the average increases. Combining forecast models holds considerable promise for operations. As Makridakis and Walker state “Combining forecasts seem to be reasonably practical alternatives when, as is often the case a true model of the data-generating process or single best forecast method cannot or is not, for whatever reason, identified.” ** **

**Behavioral Dimensions of Forecasting: **To understand some of the dimensions of forecasting, it is wise to consider human behaviors, because forecasts are not always made with statistical models. Individuals can and do forecasts by intuitively casting forth past data, and they often intervene in other ways in the statistical forecasting procedure as well. A manager may feel that item forecast generated by models must be checked for reasonableness by qualified operating decision makers. Forecasts generated by models should not be followed blindly; potential cost consequences must be considered. Decision makers can take into account qualitative data that are not in the model. Decision makers should use the forecasting model as an aid in decision making; they should not rely totally on the forecasting models for all decisions. Many, perhaps most, forecasts for production/operation management are individual intuitive forecasts. ** **

**Intuitive Forecasting as a Judgmental Process: **Currently, little is known about the effectiveness of intuitive forecasting. We can, however, analyze some of the mental processes involved. A forecast may be regarded as the culmination of a process consisting of several stages, including information search and information processing. It results in human inferences about the future that are based on particular patterns of historical data presented to the forecaster. We can speculate about a number of environmental factors that may affect intuitive forecasting.** **

**Meaningfulness**: Forecasting requires considering a restricted set of information about historical demand. When we discuss job enrichment and job design we see that if repetitive tasks can be made meaningful to the person performing them, positive effects usually result. Imparting meaningfulness to the task of forecasting, then, may be expected to affect the reliability of intuitive forecasting task, the more accurate the intuitive forecast.

**Pattern Complexity: **Pattern complexity, the shape of demand pattern, is in general, a critical variable in intuitive forecasting, just as it is in model forecasting. Some behavioral studies suggest that intuitive forecasts may perform better on a linear than on non-linear demand patterns. In addition, people apparently try to use the non-linear date in a linear manner.

**The degree of Noise: **Given sufficient historical data, the forecasting problems are trivial for most cases without noise. Introducing random variations, however, often it brings about a condition called cue uncertainty. Very high noise levels obscure the basis for accurate forecasting, and often the result is lower forecast accuracy.** **

**Individual Variability: **Another finding in intuitive forecasting studies which is the wide variability of performance of the forecasters. When comparing forecasters with models, there are typically a few very good forecasters, but there are even more very poor forecasters. If planning and directing production and operation are based on poor intuitive forecasts, these variations in performance can be very expensive.

**Individual versus Model Performance: **How do individuals compare to naïve forecasting models? In studies, exponential smoothening models, when fit to the historical demands given to intuitive forecasters significantly outperformed group average performance. Only a very few good intuitive forecasters outperformed the models. The operation manager would be wise to consider models as an alternative to individuals. Models generally are more accurate, and if a large number of items must be forecast, the models are more economical.

**Forecasting, Planning, and Behavior** An excellent literature review and evaluation compare many modeling and psychological dimensions of forecasting, planning and decision making. Many information processing limitations and biases involving human judgment apply to forecast and planning as well. Errors in forecasting procedures are caused by using redundant information, failing to seek possible disconfirming evidence, and being overconfident about judgments. In addition, numerous studies show that predictive judgment of humans is frequently less reliable than that of simple quantitative models. ** **

**Forecasting and the Indian Scenario: **Some of the more creative and productive organizations in India are to be found among high technology organizations such as Atomic Energy Commission, Indian Space and Research Organization, Bharat Heavy Electrical and Defense Research and Development Organization (DRDO) The participation of private sector in the high technology area has been very limited. The high technology companies in India have been scanning for technology development in the world and trying to develop indigenous equivalent products. And for this, they do forecasting, particularly that of technology, in some measures.

However, barring these few examples, by and large, other organizations have not been using forecasting in a scientific manner. The reasons could be many. One of the main reasons has been that they do not feel the need to survey the environment and forecast future business. The reason behind this has been the country’s erstwhile closure of foreign participation, ensuring secure markets for domestic companies. India has been a seller’s market at least for past half a century. If you could produce something, it could always be sold in a product-starved country.

The situation has changed since the turn of the century but old habits, beliefs, and psychology take time to change. The emphasis, therefore, had been on producing rather than on real proactive marketing. The environmental scan of business /industries stopped at that. Hence, forecasting had indeed been a neglected aspect of management. Now, with the gradual opening up of the economy, the economic scenario has changed due to the increasing participation of the multinational corporations in various areas of business/industry., including infrastructure. The Indian economy is increasingly getting the characteristics of a buyer’s market. The Indian businessman, therefore, has to be very alert about the mumblings in the gangways.

Forecasting models, such as the causal models can now be used to forecast the effect of concession on the corporate tax, customs duty, excise and other areas. Opinion based methods such as Delphi techniques and consumer behavioral surveys have increasing relevance. Monopoly or oligopoly does not need forecasting. Indian industries and businesses are waking up to the fact that it is now a different game. They know that if they do not follow appropriate management basics such as forecasting they risk the danger of being marginalized for a long time to come.