A small company sells medical supplies to hospitals. Management wants to assess
ID: 1202887 • Letter: A
Question
A small company sells medical supplies to hospitals. Management wants to assess the efficacy of the company’s advertising, and an analyst has produced the following three regressions:
salesi = -516.4+ 2.47 advertisingi+ 1.86 bonusi +ei
salesi = -156.5+ 2.77 advertisingi +ui
bonusi = 193.5 +0.16 advertisingi +vi
where salesi are sales in location i (in $1,000), advertisingi is spending on advertising (in $ 100), and bonusi is the amount of bonuses paid to sales people in location i (in $ 100).
(a) Why is the coefficient on advertising different in the first two regressions? Show how the coefficient in the second regression relates to the one in the first using the information provided.
(b) Is either of the regressions likely to provide a good indication of the causal effect of advertising spending on sales? Why or why not?
Explanation / Answer
The coefficient on advertising different in the first two regressions because in the first equation their is one more Independent variable (bonusi) which is explaining the sales in location i but this variable Bonus is correlated to the Advertizing variable, and thus could be decuced into Advertizing variable in the following way
salesi = -516.4+ 2.47 advertisingi+ 1.86 bonusi +ei
Now bonusi = 193.5 +0.16 advertisingi +vi , Putting it into the above equation
salesi = -516.4+ 2.47 advertisingi+ 1.86 ( 193.5 +0.16 advertisingi +vi ) +ei
salesi = -516.4+ 2.47 advertisingi + 359.91 + 0.30 advertisingi +ui
So, salesi = -156.5+ 2.77 advertisingi +ui . Which is the given second equation
No, Neither of the regressions is likely to provide a good indication of the causal effect of advertising spending on sales because here the two explanatory variables (i.e Advertizing and Bonus) overlap completely, with one a perfect linear function of the others, such that the method of analysis cannot distinguish them from each other. This condition will prevent a multiple regression from estimating coefficients; and hus the equation becomes unsolvable due to existance of full multicollinearity.
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