Nopane Advertising Strategy Analysis

Questions:

1. What does Regression 1 in the case say about the merits of “emotional” vs. “rational” copy?  What does Regression 3 say about the two types of copy?  What is the interpretation of the coefficient on copy in Regression 1?  Regression 3?

 

        In Regression 1, the estimated coefficient on the “Dum Copy” variable is 2.134.  Since Dum Copy = 1 if the “emotional” copy is used, and = 0 if the “rational copy is used, a positive coefficient would indicate that the “emotional” copy results in higher average sales than the “rational” copy.  However, we should note that the t-value associated with the hypothesis test with null hypothesis that the true coefficient on Dum Copy = 0 is 1.1.  The degrees of freedom associated with this t-value are n - # of coefficients estimated = 19.  Therefore we can determine the corresponding p-value to be 0.285.  (Note that if we actually calculated the t-value by dividing 2.134 by 2.027, we get a number closer to 1.05 than to 1.1.  The 1.1 in the case just comes from rounding up.  So really, a more exact p-value is the one corresponding to a t of 1.05, or p-value = 0.306.)  Thus, even though the estimated coefficient is positive, our hypothesis test tells us that the evidence that it is different from zero is not very strong.

        Similarly, in Regression 3, the estimated coefficient on Dum Copy is -3.00.  This indicates that the “rational” copy seems to give higher average sales than the “emotional” copy.  The t-value given here is -1.7 and the number of degrees of freedom = 20.  Therefore the associated p-value for the hypothesis test with null that the true coefficient equals 0 is 0.1046.  Thus, while still not overwhelmingly strong, we do have moderately strong evidence that the true coefficient is different from zero.  In particular, if we wanted to prove that the true coefficient on Dum Copy in Regression 3 was less than zero, the corresponding p-value would be 0.0523, indicating only about a 5% chance of making a mistake if we conclude that the true coefficient is less than zero.

        These two coefficients, then, seem quite different.  How can this be?  The key to understanding is to interpret the meaning of the coefficient on Dum Copy in the two regressions and see the difference in interpretation.  In Regression 1, the coefficient on Dum Copy tells us the average additional sales per 100 prospects that we would expect if we switched from using the “rational” copy to using the “emotional” copy, holding fixed the amount of Nopane ad spending, the amount of our competitors’ ad spending, and the Segment where the sales territory is located.  In Regression 3, the coefficient on Dum Copy tells us the same thing except our competitors’ ad spending is not held fixed.  (We can see this because the only difference between the two regressions is that the Competition variable is not included in Regression 3.)  Thus Regression 1 predicts 2.134 additional sales per 100 territories, on average, holding the three other variables fixed, for the “emotional” copy as compared to the “rational” copy.  Regression 2 predicts an average loss of 3 sales per 100 territories, holding Segment and our ad spending fixed, for the “emotional” as compared to the “rational” copy.

(Note: As we have seen, it is important to check the plot of residuals vs. fitted values and run a BP test when you look at a regression.  Doing so for Regressions 1 and 3 turns up essentially no evidence of non-constant variance (very high p-values for the BP test) and no distinct curvature, so things look pretty good as far as our regression assumptions go.)

2. Assuming Alison Silk's hypothesis is correct, which of the regressions is most relevant for choosing an advertising strategy?  Why?

        Ms. Silk suggested (see p. 3 of the case) that Nopane's competitors might react to a national strategy by Nopane in a way very similar to their reaction in the advertising experiment.  If this is true then Regression 3, the regression leaving out the "competitors' advertising" variable, is the most relevant one.  Why? Think about what it means to set a national advertising strategy for Nopane -- choosing both ad copy and an advertising spending level.  To help in choosing a strategy, the question that needs to be answered for each strategy is: what will happen to sales if this strategy is implemented?  We can use Regression 3 to provide an answer (for each Segment, A and B) by plugging in the values corresponding to the copy and the Nopane advertising spending under the given strategy.  For example, this method predicts that running the "emotional" copy and spending $4.75 per 100 prospects will yield an average of 28.66 unit sales per 100 prospects in Segment A (on the coasts) and 28.83 units in Segment B (the middle of the country).  The prediction for "rational" copy and $2.50 per 100 prospects is 29.42 (region A) and 29.59 (region B).  Regression 1 cannot be used directly for this prediction, since we do not know the values of competitors' advertising to plug-in under the various strategies.

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        Q: But what about omitted variable bias?  We can see from regression 2 that competitors’ advertising spending seems related to our copy and ad spending.  Doesn't this mean that the estimated coefficients on copy and ad spending in regression 3 are biased?

        A: Yes, we would expect the coefficient estimates to be biased.  However, recall the nature of the bias: the coefficient estimates reflect not only the effect of the variable included in the regression (holding other included variables fixed) but also include the effect of any variables left out of the regression, to the extent that they are ...

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