Question

1. Manager do not like future uncertainty.  Most managers use forecasting, prediction, and estimation to minimize uncertainty. Suppose you have a linear demand function for product X: Q = a + b•P_x+c•P_y+ d•M, where Q is sales of X, P_xand P_yare the price of products X and Y, and M (consumer’s income).

(a) What does the coefficient for each independent variable mean?

(b) How would you conduct inference from the regression coefficients?

(c) How should we determine the choice of forecasting technique?

Answer 1

Independent variables are: Prices of product x and y: Px and Py and consumer income: M

dependent varible is Q: sales for product X

Coeffcients: slope of the function: b,c,d

Intercept of the function: a is a constant

a)Coefficient of each independent variable represent the slope of the regression line. It shows that if the independent variable increases by 1 unit, how much would the dependent variable change.

b) Inference would be as follows:

If the p-value of a coefficient is less than the chosen significance level, such as 0.05, the relationship between dependent and independent variable is statistically significant. This means the variation in dependent variable is significantly explained by the repsective variable whose p-vale of the coefficient is less than 5%. The sign of the coefficient would tell us the direction of relationship between dependent variable and the respective independent variable, whether its positive(+) or negative(-).

Example: If b is - 5% and its p value is 0.03 then, we can say that 1% increase in price of X causes 5% fall in sales of X. Thus, Px is a statistically significant variable in the model explaining the variation in dependent variable.

c) The selection of a method depends on many factors—the context of the forecast, the relevance and availability of historical data, the degree of accuracy desirable, the time period to be forecast, the cost/ benefit (or value) of the forecast to the company, and the time available for making the analysis. Further, the stage of the product’s life cycle for which it is making the forecast is important. The availability of data and the possibility of establishing relationships between the factors depend directly on the maturity of a product, and hence the life-cycle stage is a prime determinant of the forecasting method to be used.

The forecaster should choose a technique that makes the best use of available data. If the forecaster can readily apply one technique of acceptable accuracy, he or she should not try using a more advanced technique that offers potentially greater accuracy but that requires nonexistent information or information that is costly to obtain. Techniques vary in their costs, as well as in scope and accuracy. The forecaster must fix the level of inaccuracy he or she can tolerate—in other words, decide how his or her decision will vary, depending on the range of accuracy of the forecast. This allows the forecaster to trade off cost against the value of accuracy in choosing a technique. Also,the purpose of the forecast—how is it to be used - determines the accuracy and power required of the techniques, and hence governs selection criteria. Further, examining how important is the past in estimating the future is also important.