Nopane Factors

1
Nopane Factors

• Sales Unit sales of Nopane per 100 prospects.
• Nopane Ad Dollars Number of dollars per 100
  prospects spent on Nopane advertising.
• Competition Number of dollars per 100 prospects
  spent by competitors advertising.
• Dum Copy 1 if emotional copy is used.
• Dum Segm 1 if sales territory is in Segment A.

2
Regression 1
3
Regression 3
4
Question 1

• What Regressions 1 and 3 say about the merits of
  emotional vs. rational copy?
• What is the interpretation of the coefficient on
  Dum copy in Regressions 1 and 3?

5
Ans. Q 1

• What Regressions 1 and 3 say about the merits of
  emotional vs. rational copy?
• Regression 1. The coefficient on Dum Copy is
  2.13. The p-value is 0.3. There is very weak
  evidence the true coefficient is non-zero.
• Regression 3. The coefficient on Dum Copy is
  -3. The p-value is 0.1. There is some evidence
  that the true coefficient is non-zero.

6
Ans. Q 1(cont.)

• What is the interpretation of the coefficient on
  Dum copy in Regressions 1 and 3?
• Regression 1. The coefficient on Dum Copy is the
  average additional sales per 100 prospects if we
  switched from rational copy to emotional
  copy, holding fixed all variables.
• Regression 3. The coefficient on Dum Copy is the
  same thing except that our competitors ad
  spending is not held fixed.

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Question 2

• Assuming Alison Silk's hypothesis is correct,
  which of the regressions is most relevant for
  choosing an advertising strategy?
• Silks Hypothesis Nopanes competitor will react
  to our national strategy(whatever it might be) in
  the same way as they did in the test.

8
Ans. Q 2

• Regression 1 requires knowledge of Competitors
  spending
• We do not know this with Certainty so use
  Regression 3

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OVB analysis

• What does regression 2 say about the Omitted
  variable bias when competition is left out of
  regression 3?
• We will extract the bias related to the variables
  Ad Dollars, DumSegm, and DumCopy one at a time

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OVB for Ad dollars

• By regression 2 holding all other factors fixed
  we have
• Comp.8515AdDollarsC1
• Thus we see indirectly that (on average) each
  dollar spent by Nopane on advertising results in
  .8515 dollars spending by competition
• i.e. c2.8515, and as expected there is a
  positive correlation between the two.

11
OVB for Ad dollars cont.

• Furthermore from regression 1, b2 is the
  coefficient of Competion which is
• b2-.5652
• Recall that b2 represents the effect of
  competitions ad spending on NOPANE sales. This
  has a negative effect /per dollar spent , as
  expected.
• Bias (-.5652)(.8515).9959-1.477

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OVB on NoPane add spending in Regression 3

• Using the bias calculation we see that
• .9599AdDollars1.477Ad Dollars (-.5652)(.8515)AdD
  ollars
• Where the second terms corresponds to the
• (the effect of competition on sales )(the
  effect of nopane add spending on competition
  spending)

13
OVB on NoPane add spending in Regression 3

• In this case, examining Regression 1 and 3 we see
  that even though we have omitted competition from
  regression 3 the effect of competition is
  incorporated in an appropriate way in the
  coefficient of NoPaneAdDollars spending.
• That is to say the bias effect is not
  counterintuitive.

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OVB on Copy type (DumCopy)

• Similar to our previous analysis we can get
• From regression 2, if we run emotional copy this
  adds(on average) an additional c29.083 dollars
  to competitions ad spending
• Note that the effect of competition on sales is
  still b2-.5652 from regression 1
• Bias-3-2.134(-.5652)(9.083)
• Hence the coefficient in regression 3 is
• -3(-.5652)(9.083) 2.134

15
OVB on Copy type (DumSeg)

• Similar to our previous analysis we can get
• From regression 2, if we are in segment A this
  adds(on average) an additional c2.9167 dollars
  to competitions ad spending
• Note that the effect of competition on sales is
  still b2-.5652 from regression 1
• Bias-.1667-.3514(-.5652)(.9167)
• Hence the coefficient in regression 3 is
• -.1667 (-.5652)(.9167).3514

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Comments

• We see that while there is obviously OVB, its
  effect does incorporate the behavior of the
  competitors spending in regression 3.
• So this should be a bit comforting if we cannot
  exactly anticipate the competitors spending
• Of course regression 3 has its limitations as its
  adjusted R-squared is only 22.53 so the model is
  not fully satisfactory

17
Comments

• Note that that when we include competition in the
  regression, i.e. going from Regression 3 to
  Regression 1. the adjusted R-squared becomes
  50.54
• It is a substantial improvement but indeed there
  is some room for further improvement
• Furthermore if we cannot measure the true
  response of the competition then Regression 1
  cannot be used
• Perhaps Competition is also correlated with other
  variables we have not considered yet? This might
  help us if we cannot easily anticipate what
  exactly the competition will do in terms of a
  dollar amount for pricing

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Why cant we use regression 2 to predict what the
competition will spend?

• There are several issues
• One is that the adjusted R-squared for Regression
  2 is only about 50.68
• This means that regression 2 does not account for
  50 of the variability in the competitions
  advertising spending
• So statistically speaking we could wind up with a
  value that is highly unreliable.
• Furthermore there are issues that arise when
  trying to use the same dataset to both estimate
  regression coefficients and predict independent
  variables.

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Cont.

• We could take an informal approach(clearly
  non-statistical) and look at the data in Exhibit
  1 p.20 on Competition Ad Expend.
• But notice that the competitor does not quite
  react the same way every time
• For instance the first data set has Nopane
  spending 2.5 on emotional copy in segment A and
  the competition spends 16
• In the second entry of data Nopane does precisely
  the same thing but now the competition spends 20
• So it becomes difficult to guess what value they
  will use in the future.
• However note that in both cases 26 Unit sales
  were made. So maybe other factors are at work

20
Cont-quandary

• One could still try to run regression 1 with
  different values for competition but unless you
  are really sure and can prove it, you are running
  the risk of offending your boss-Vice President
  Stanley.
• On the other hand if you use Stanleys
  recommendation (which might be wrong) you run the
  risk of losing money for the company. Naturally
  you might be blamed rather than Stanley.

21
Cont.

• This is why Silk wants to find a way of avoiding
  a model that requires an explicit number for
  competitions ad expenditure.
• Ideally if both models agree then she would feel
  more comfortable
• But at present Regressions 1 and 3 are both
  inadequate.
• Return to this point in question 4.

22
Example using regress 3

• If we ran the emotional copy and spent 4.75
  per 100 prospects the average sales would be
  28.66 per 100 prospects in seg A(coasts) and
  28.83 units in Seg B(the middle).
• For rational copy and 2.50 per 100 prospects is
  29.42 for A and 29.59 for B

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Question 3

• Answer all the questions in 2 assuming that
  Stanley Skamarycz's hypothesis is correct.
• Regression 1 is the appropriate choice.
• Mr. Skamarycz believes that he can accurately
  specify competitors' behavior (19 per 100
  prospects always). So, we estimate our strategy
  holding the competitors ad spending fixed.

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Question 4

• What national ad strategy do you advocate?
• Assume an additional unit sold per 100 prospects
  over a six-month period yields a profit (net of
  production and delivery costs, but not net of
  advertising costs) of 10 dollars per 100
  prospects over a six-month period.

25
Cont.

• The break even point is given as follows
• Suppose we spend 10 in advertising then
• The we break even if the beta coefficient
  satisfies
• 10b1
• That is b.1.
• For Reg 1, we get Profit 14.77(10)-10

26
Cont.

• This suggests that in either case we should spend
  the maximum of 8 of advertising per 100
• But Regression 1 suggests we should use Emotional
  copy, while regression 3 suggests Rational Copy.

27
Cont.

• The regressions assume the effect of ad
  expenditure is equal for both ad copies.
• i.e. No slope dummy variable for ad type
• They also assume that copy and ad expenditure is
  equally effective across regions.
• No slope dummy variable for region
• Let try these

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Question 4

• We must add slope dummy variables
• (Nopane ad dollars)(Dum Copy),
• Additional effect of emotional copy
• (Nopane ad dollars)(Dum Region),
• Additional effect of segment A
• I also added
• (Dum Copy)(Dum Region).
• The modified regressions 1 is

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Modified Regression 1
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Modified Regression 1

• Competition is not significant. Our analysis is
  similar with and without competition.
• The coefficients on segments are not significant.
  Our analysis is similar in both regions.
• Nopane Addum copy is significant.
• Increasing ad spending does help when running the
  "rational" copy.

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Modified Regression 3
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Predictions for different policies (Segment A)

• Policy 8.00 ad spending, "rational"
  copypredicted value of Unit Sales 39.54994
• Policy 4.75 ad spending, "rational"
  copypredicted value of Unit Sales 31.47646
• Policy 2.50 ad spending, "rational"
  copypredicted value of Unit Sales 25.88713

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Predictions for different policies (Segment A)

• Policy 8.00 ad spending, "emotional"
  copypredicted value of Unit Sales 29.4741
• Policy 4.75 ad spending, "emotional'
  copypredicted value of Unit Sales 28.7218
• Policy 2.50 ad spending, "emotional"
  copypredicted value of Unit Sales
  28.20098

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Question 4

• The "rational" copy and the highest level of ad
  spending is best.
• Profits are 39.55 (10) - 8.00 385.50 per
  100 prospects in Region A.
• Similar results obtain if we use modified
  regression 3 (not controlling for competition)
  and also for Segment B.

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Question 5

• Instead of a national campaign, Ms. Silk
  considers one campaign for the East and West
  Coast states and another for the middle of the
  country. Comment on the desirability of
  splitting up the campaign.
• Our analysis shows that the best strategy is the
  same in both regions. The rational copy
  spending 8.00 per 100 prospects.

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Last comment

• One can run diagnostics to determine if the high
  p-values we see are due to multicollinearity or
  are actual
• Furthermore one can run F-tests to check the
  joint significance of suspect independent
  variables.
• In the models incorporating slope dummy variables
  we now see that competition spending and market
  segment are not highly significant factors given
  the rest of the variables.