The problem being investigated is the reason for the existence of confusing facts in the analysis of sales obtained amidst expenses of advertising, promotion. A regression model has been formulated to clear the state of confusion. There is the problem of determining whether advertising and promotions have any benefits that add up to the sales increase. Previous administrations tried several strategies that bore no fruits. It has not yet been clear on this issue. There is also the confusion of the sale of the meat loaf mix where some people claim that it seems to sell better when bad economic times exist arguing that that is the time when the relatively cheap product was selling well. Regression analysis is aimed at discovering relationships between variables in an expression. The dependent variable has a given relationship with each and every independent variable. In a regression expression, there is a dependent variable which equals the constant variable added to all the independent variables which are solely multiplied by their respective coefficients.
A regression model has been formulated as Y=883.52+5.21X1+3.11X2-5.63X3 where the dependent variable Y is the sales made in a given period. X1 stands for units used for promotion; X2 stands for the units used in advertising, and X3 stands for the units of economic indices. The data in this regression model are sampled from previous 24 quarters. Advertising, promotions and economic indices per every quarter are recorded so as to aid in future endeavors. The coefficient of advertising has an estimated standard error of 1.07, a t-statistic of 2.91 and a p-value of 0.0087. It is therefore deemed insignificant at 95% confidence interval. Promotion has an estimated standard error of 1.13, a t-statistic of 4.6 and a p-value of 0.0017 which can be concluded that promotion is insignificant at 95% confidence interval. From the analysis, it is clear that advertising and promotions are not significant to the sales that are made in a given period. Hence, the lack of change in any increases or decreases in amounts of resources channeled towards advertising and promotions (Montgomery et al., p.6).
About the forecasting for the next two-quarters AFP plans to commit as follows;
Advertising: Next quarter - $30, subsequent quarter - $10
Promotion: Next quarter - $10, subsequent quarter - $25
Economic Index is 115 for both quarters
Next quarter forecast;
Y=883.52+5.21(30) +3.11(10)-5.63(115)
Y=883.52+156.3+31.1-647.45
= $423.47
Subsequent quarter forecast;
Y=883.52+5.21(10) +3.11(25)-5.63(115)
=883.52+52.1+77.75-647.45
=$365.92
The coefficient of determination, R2=1-residual SS/ total SS =1-0.650547202 = 0.349. This value 0.349 shows that the data is less fitted by a line of best fit. The coefficient of determination runs from 0 to 1 where a zero signifies that the line does not fit the data while a 1 shows that the line perfectly fits the data. The hypothesis can be tested either by using the p-value approach or by using the critical value approach. The p-value approach is used in this paper. The data has been tested at 95% confidence interval. The regression formula is usually Y=B0+B1X1+B2X2+B3X3+e where Y is the dependent variable, B0 is the constant, B1, B2, and B3 are coefficients of the variables, and X’s are the independent (exploratory) variables. The best advice would be first to stop advertising and promotions and first focus on products processing since advertising and promotions are now redundant and cannot show any change even when added or deducted (Chatterjee et al., p.24).
Work cited
Chatterjee, Samprit, and Ali S. Hadi. Regression analysis by example. John Wiley & Sons, 2015.
Montgomery, Douglas C., Elizabeth A. Peck, and G. Geoffrey Vining. Introduction to linear regression analysis. John Wiley & Sons, 2015.
