Your firm is attempting to learn the effectiveness of a newly developed television ad on its sales. To do this, it has randomly run the ad between 0 and 5 times during one week across a large number of television markets in the United States. It then recorded product sales for the following month for each market. To conduct the analysis, analysts at the firm have assumed the following data-generating process:

Salesi=?+?Adsi+Ui

Regressing Sales on Ads yields ?ˆ=350. The firm would like to use this number to project the change in Sales when increasing weekly television ads to 20.

   1. According to these results, what is the expected change in Sales when Ads increase from 5 to 20?
   2. Why should we be skeptical of our result from Part a?
   3. What can you do to find an estimate of the effect of increasing Ads from 5 to 20 that is more credible?
 

 

Regression Analysis

Regression analysis is instrumental in quantifying and estimating the relationship between two or more variables. For example, the regressing sales prompted by ads in the television market contain numerous variables. However, in this context, the variables have been reduced to three. Initially, the number of ads run per week in different television markets was 0 to 5 before increasing to 20. 

Analysis.

Question 1. According to these results, what is the expected change in sales when Ads increase from 5 to 20?

In this regression analysis, the most predominant variable is the number of Ads run by the firm per week. This variable is directly proportional to the generated sales. As such, the number of sales is expected to increase with an increase in the number of Ads per week.

Question 2. Why should we be skeptical of our result from part a?

Despite being directly proportional to sales, the number of Ads cannot be used to directly estimate the number of sales. Other innumerable factors have also not been considered in this analysis. Therefore, the results of this analysis can only be used as estimates to merely guide the firm's marketing.

Question 3. What can you do to find an estimate of the effect of increasing Ads from 5 to 20 that is more credible?

            The accuracy of the regression analysis largely depends on the estimates used for the analysis. Additionally, more independent variables increase the accuracy of an analysis (Freund et al., 2006). In this context, since the results of the first analysis are used in the second, then the first analysis should be done using an exact number of Ads instead of a range of 0 to 5. Ultimately, this would increase the accuracy in the subsequent analysis.