### A.4 Uncertainty

```Readings
Baye 6th edition or 7th edition, Chapter 3
BA 445 Lesson A.4 Uncertainty
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Overview
Overview
BA 445 Lesson A.4 Uncertainty
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Overview
Expected Value distinguishes good decisions from good luck. Gambling with
positive expected value virtually guarantees long-run success. — So, make good
decisions and patiently wait for success.
Confidence Intervals can test whether business success resulted from good
decisions, and whether failure resulted from bad decisions. — So, test
successes and failures to evaluate decisions.
Regression Analysis can test whether demand is more likely linear or log-linear,
and can estimate which coefficient values are more likely. Those estimates then
affect predictions and decisions.
BA 445 Lesson A.4 Uncertainty
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Before class, be sure Analysis ToolPack is added in to
Excel.
• Click Excel options
• You should see Analysis ToolPack listed
http://faculty.pepperdine.edu/jburke2/ba445/PowerP1/SimGamble.xlsx
http://faculty.pepperdine.edu/jburke2/ba445/PowerP1/MultiRegression.xlsx
BA 445 Lesson A.4 Uncertainty
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Expected Value
Expected Value
BA 445 Lesson A.4 Uncertainty
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Expected Value
Overview
Expected Value distinguishes good decisions from good
luck. Gambling with positive expected value virtually
guaranteeing long-run success. — So, make good
decisions and patiently wait for success.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Gambling
• Gambling is risking money or anything of value with the
goal of winning additional money or value.
• Most business decisions (what to produce, what to
charge, who to hire, what to pay, …) involve gambling.

For example, you produce today but the price you can charge
customers can change in the future, so your profit is risky.
• Most consumption decisions also involve gambling.


your house burns, you win; if it does not burn, you loose.
Flanders from the Simpsons does not have fire insurance on his
house because “it’s too much like gambling”.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Gamblers verses Entertainment Seekers and Thrill Seekers
 Good poker players in Las Vegas may be good
gamblers (seeking money). Good gamblers avoid
they can win against good players) or can be thrill
seekers or entertainment seekers.
 A bad poker player that looses then says “at least I
had fun” is an entertainment seeker.
 Keanu Reeves is a well-known thrill seeker. He
survived a near-fatal motorcycle crash in 1988 and
still bears the scars of another accident in 1996.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Risk Aversion
• Whether you should gamble may at first seem to depend
on whether you are a risk taker or a risk avoider. (But
we will see it often does not.)
• A risk taker allows possible gains to offset possible loses
from a gamble.
• A risk avoider focuses on avoiding loss.
• For example, propping open fire doors (say, on the third
floor of CCB) gains time but could lead to loss of life.
Risk takers would prop open the doors but risk avoiders
would not.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Repeated Risk
• Gambling risk depends on whether one gambles just
once, or many times.
• Gambling your life savings on one hand of blackjack
generates significant risk.
• Gambling your life savings divided into thousands of
good gambles generates little risk, like playing
thousands of hands of blackjack if you have an
BA 445 Lesson A.4 Uncertainty
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Expected Value
Expected Value
• How do you identify a good gamble?
• Expected value (EV) is the sum of probabilities times
payoffs.
• Positive expected value identifies a good gamble. We
will see that most people should take good gambles.
• Negative expected value identifies a bad gamble. We will
see that most people should avoid bad gambles.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Example
• Is roulette a good gamble?
• Any player placing \$1 on a number (which is one number
out of 38 possible, counting 0 and 00) can earn \$35
profit, so expects EV = (1/38)(35) + (37/38)(-1) = -\$2/38
<0
BA 445 Lesson A.4 Uncertainty
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Expected Value
Example
• Is poker a good gamble?
• Since the casino (the house) takes a payment (rake), the
sum total of the EV of each player is negative, so at least
one player expects EV < 0 (the sucker)
• If you can’t spot the sucker in the first half hour at the
table, then you are the sucker.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Example
• Is rolling through a stop sign a good gamble?
• Rolling through a stop sign gains valuable time if you are
not caught and looses both time and money if you are
caught and ticketed. So, EV = Prob.(not caught)(Gain) +
Prob.(caught)(Loss) can be either positive or negative.
• In Prof. Burke’s experience, it is positive at Pepperdine.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Example
• Is rolling through a car gate a good gamble?
• Rolling through a car gate gains valuable time if you are
not crushed by the gate that has not yet opened and
looses both time and money if you are crushed. So, EV
= Prob.(not caught)(Gain) + Prob.(caught)(Loss) can be
either positive or negative.
• In Prof. Burke’s experience, it is positive exiting the
parking lot Pepperdine’s CCB building.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Example
• Should you gamble \$1 of value if there is a 55% chance
of winning \$1 and a 45% chance of loosing \$1?
• If you are young, this is a practical question because
looking for something you lost in your yard, gambling
your gas looking for a better parking spot,…).
BA 445 Lesson A.4 Uncertainty
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Expected Value
Simulation
• Should you gamble \$1 of value if there is a 55% chance of winning
and a 45% chance of loosing?
• If you gamble only once, there is a 45% chance you will loose.
• If you gamble 1000 times, then all of the simulations in the Excel file
SimGamble.xls should report a win because the expected value =
.55(+\$1) + .45(-\$1) = \$.10 is positive.
Conclusion
• Avoid bad gambles (Vegas, the lottery, purchase protection plans,
…)
• Accepting good gambles (arriving at the airport 50 minutes early
rather than 1 hour early, looking for better parking,...) virtually
guarantees long-run gains.
• Exception: You may choose a few bad gambles (unsubsidized
health insurance) if you cannot afford to lose.
BA 445 Lesson A.4 Uncertainty
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Expected Value
Good decisions
• Accepting good gambles is good decision making.
• Focus on making good decisions, and do not be
distracted by the outcome. You are virtually guaranteed
long-run success.
 Playing the lottery is a bad decision (it has negative
expected value).
• Playing just one time might produce a good outcome.
• Playing frequently virtually guarantees long-run loss.

Investing in the stock market can be a good decision
(it can have positive expected value).
• Investing just one time might produce a bad outcome.
• Investing frequently virtually guarantees long-run success.
BA 445 Lesson A.4 Uncertainty
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Confidence Intervals
Confidence Intervals
BA 445 Lesson A.4 Uncertainty
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Confidence Intervals
Overview
Confidence Intervals can test whether business success
resulted from good decisions, and whether failure resulted
from bad decisions. — So, test success and failures to
evaluate decisions.
BA 445 Lesson A.4 Uncertainty
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Confidence Intervals
• Have you been making good or bad decisions?
• The Excel file MultiRegression.xls lists the net results of
100 gambles, and tests whether those results were
coming from good gambles (with positive expected
value).
• The test is based on the regression equation
p=a+e



p is your profit from a gamble,
e is the uncertain, unpredictable, uncontrollable random
outcome (like the draw of a card) with zero expectation
a is the regression constant
• Expected profit p equals coefficient “a” (since expected e = 0)
• a > 0 means your gambles have positive expectation
• a < 0 means your gambles have negative expectation
BA 445 Lesson A.4 Uncertainty
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Confidence Intervals
Gamble Test Summary Output
 p=a+e
 The results estimate a = -.853
 The 95% confidence interval for a is -1.966 to .258
 Since the interval contains both positive and negative
numbers, there is not enough data to determine whether
or not those gambling results were coming from good
gambles.
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Regression Analysis
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Overview
Regression Analysis can test whether demand is more
likely linear or log-linear, and can estimate which coefficient
values are more likely. Those estimates then affect
predictions and decisions.
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Regression Analysis
• In addition to constants, regression analysis can estimate
coefficients of variables (correlation coefficients)
• One use is for estimating or measuring demand functions.
• Important statistics:

Confidence Intervals and t-statistics.
• Measures the significance of estimates

R-square or Coefficient of Determination, and F-statistic.
• Determines whether the model is better than no model.
• Determines whether one model is better than another model.
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Question: Passage of the 1983 Dairy Product
Stabilization act lead to a tax on milk producers. The tax
was used to advertise milk. However, the tax was later
ruled unconstitutional, and so milk advertising decreased.
To assess the likely impact on milk consumption, consider
the following data on the weekly consumption of milk (in
millions of gallons), weekly price per gallon, and weekly
expenditures on milk advertising (in hundreds of dollars).
http://faculty.pepperdine.edu/jburke2/ba445/PowerP1/MultiRegression.xlsx
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Use Data Analysis in Excel to perform two
regressions:
• Linear Q = a + b P + c A + e
• Log Linear ln(Q) = a + b ln(P) + c ln(A) + e
Determine which model better fits the data. Suppose that
the weekly price of milk is \$3.10 per gallon, and weekly
advertising falls 25 percent to \$100 (in hundreds). Using
the better model, estimate the weekly quantity of milk
consumed after the court’s ruling.
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
 The competing equations are:
 Linear Q = a + b P + c A + e
 Log Linear ln(Q) = a + b ln(P) + c ln(A) + e
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Linear Regression Summary Output
 Q=a+bP+cA+e
 R2 = 0.5472 and Adj.R2 = 0.5379, where greater
coefficients of determination indicate the data better fits
the linear regression line
 F = 58.6092, where the greater that F-statistic, the better
the data fits the linear regression line
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Log-Linear Regression Summary Output
 ln(Q) = a + b ln(P) + c ln(A) + e
 R2 = 0.4014 and Adj.R2 = 0.3891, where greater
coefficients of determination indicate the data better fits
the linear regression line
 F = 32.5221, where the greater that F-statistic, the better
the data fits the linear regression line
BA 445 Lesson A.4 Uncertainty
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Regression Analysis
Conclusion:
 The linear model better fits the data, with higher
values of all three statistics: R2, Adj.R2, and F.
 Under the linear model, at P = \$3.10 and A = \$100,
estimated milk consumption is 2.029 million gallons
per week :
Q = 6.52 – 1.61(3.10) + .005(100) = 2.029.
BA 445 Lesson A.4 Uncertainty
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Review Questions
Review Questions
 You should try to answer some of the review
questions (see the online syllabus) before the next
class.
request to discuss their answers to begin the next class.
 Your upcoming Exam 1 and cumulative Final Exam
will contain some similar questions, so you should
eventually consider every review question before taking