The correlation between Price and sales is large and negative for all three-time periods. What does this say about how prices Works?
The correlation coefficient shows a measure of the linear relationship between these two variables. However, this association does not imply causation, meaning that the change in one variable is not caused by the change of the other one in the opposite direction. Yet, the increasing negative value of the correlation coefficients allows us to infer from these results that when the price rises sales will decrease. This argument is supported by the level of significance of each case less than 0,01.
Explain the correlations between advertising and sales. What is happening to the advertising effect over time?
Apparently based solely on the correlation numbers the advertising has a negative effect on sales over the time. However when the level of significance is analyzed, it turned evident that these numbers are way greater than the (0.001) level of significance corresponding with a 99.0% confident level. Hence they are not significant and it is safe to conclude that the correlation numbers between advertising and sales have no effect.
Note that the inter-correlations between advertising location and prices are all zero. Why? This result support the experiment parameters established from the beginning, we were considering this variables as independents, meaning that there are no linear relationship among them, endorsing the design of the experiment.
What do the regressions of sales variables (Sales1, Sales2, Sales3) using P, A and L as independent variables, imply about the effect of prices? Of advertising? Of Location?
Effect of Price: As we stated in the question #1 there is a strong correlation between the prince and the sales numbers. An increment in price suggests a decrease in sales. So, based on this result, we may say that the market is price sensitive and the company should...