Therefore, the observed values would be different for each case, hence the difference in the results.
Coming to the problem of optimization, the only variable that is used for estimating the optimal values is known as the coefficient of multiple determinations, which is denoted by R2. According to theory, R2 is used to determine the proportion of the variation in the dependent variable that is explained by the set of independent variables. For the above 2 cases, R2 was found to be 0.546 & 0.570 respectively. This signifies that in the analysis, only 54.6% and 57% of the variation in the revenue can be accounted for by the 3 variables taken into consideration. If indeed one were to make the solution optimal, then it can only be done if the model were to explain the results in terms of the largest variation in the dependent variables along with the use of the fewest number of independent variables.
As such, it would be optimal to include all the lagged values in the regression equation (as they are dependent variables), but along with this it would also be necessary to include the normal values (current advertising expenditure as well as the price index). The estimated advertising costs (under normal values) must be excluded, as it is not required. Under this scheme, the R2 turns out to be 0,756, which is the largest obtained among all possible combinations, and hence the most optimal.
Under the following scenario, we adopt the Normal distribu ...