1)The correlation between price and sales is large and negative for all three time periods. What does this say about how price works? The negative relation shows that there is an inverse relation between price and sales. If price rises, sales go down and vice versa. 2)Explain the correlations between advertising and sales. What is happening to the advertising effect over time? In the first two periods advertising is effective and has a positive correlation with sales. This implies that sales increased as advertising increased.
However, in the last period the correlation is negative which implies if advertising increases sales will actually fall. Consumers tend to get bored with the marketing message over time. 3)Note that the intercorrelations between advertising location and price are all zero. Why? This just means that there is no linear correlation between all three variables advertising/location/price. 4)Run regressions for each sales variable (s1, s2, s3) using P, A, L and independent variables. What do the regressions imply about the effect on price?
Of advertising? Of location? In sales period one the coefficients table of the regression reveals that there is statistical significance between the price variable and sales. It is a negative correlation which implies that if price is raised there is a statistical significant chance that sales will decrease. The other variables of advertising and location have a positive correlation with sales but it is not statistical significant. In sales period two the regression shows the same effects of price on sales as in period one.
While the other two variables are again not statistical significant they are not both positive to sales in the period. The value of location actually has a negative effect on sales. In sales period three the regression shows very similar results to that of period two. However, in this period price has an even greater negative effect on sales as a statistically significant variable. 5)Rerun the regression adding the variables I and V. Do the judgments about the effects of price, advertising, and location change?
Why? When adding these variables the negative correlation effect that price held on sales for the previous question is not as strong. The coefficient is closer to zero. Advertising for this regression becomes a very strong indicator of sales having a positive correlation and is considered statistically significant. The location variable continues to have a positive correlation in this scenario. More so, then the previous question but the location variable still is not statistically significant.
The major shift we see from the previous regression is the advertising variable now has a positive effect on sales across all three time periods. In all periods, advertising holds much more statistical significance when the income and store variables are introduced. 6)If possible obtain and output of residuals (difference between model predicted Y and actual Y). Check the residuals to identify observations that do not seem to fit the model. Why don’t they fit?
The regressions for problems four and five seem to visually be very similar. When the residuals are scatter plotted though you can see a slight difference. When using an absolute value to identify outliners the second regression seems to be a tighter fit with the values closer to the mean. When income and location are added to the regression the effect that price can have is a bit diluted which keeps the results closer to the mean. 7)What additional regression runs, if any, should be made to complete the analysis of this data?
Regressions with sales of each period as the dependent variable and price, advertising, and store as the independent variables show statistical significance among all variables. This shows a negative correlation with price and positive correlation between advertising and store on sales. Recommendations: More analysis was certainly needed from the original study. From the latest analysis it can be concluded that the organization needs to adopt an advertising strategy that is heavy early on in the campaign which would then be set to decreases over time.
This is supported by the regression analysis that shows the positive correlation actually switch to negative in sales period three. A per price of 24 seems ideal due to the negative correlation on sales if it were to be increased to any of the higher price points tested. The location classification of the item has little effect as explained by the data. Our recommendation would be to market the product as a snack and a breakfast meal or it could be alternated back and forth with little effect on revenue.