SOLUTION: University Cumberlands Roles of Data and Predictive Analytics in Business Paper

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Sales
Labor Costs Materials Costs
$2,055,279.00 $38,313.00
$17,989.00
$2,238,758.00 $63,294.00
$21,659.00
$1,143,833.00 $40,570.00
$25,403.00
$1,901,107.00 $54,704.00
$24,436.00
$2,194,766.00 $52,411.00
$17,782.00
$1,329,758.00 $37,071.00
$24,827.00
$1,510,285.00 $42,391.00
$18,448.00
$2,086,502.00 $50,228.00
$20,053.00
$2,328,835.00 $42,438.00
$23,983.00
$1,950,095.00 $40,898.00
$15,993.00
$1,411,194.00 $64,093.00
$26,194.00
$2,014,357.00 $38,075.00
$24,939.00
$971,042.00 $57,975.00
$24,213.00
$1,886,358.00 $65,003.00
$22,548.00
$1,450,856.00 $65,628.00
$25,459.00
$1,324,142.00 $45,014.00
$17,893.00
$1,185,863.00 $36,088.00
$18,024.00
$1,280,627.00 $47,377.00
$24,361.00
$877,951.00 $42,295.00
$21,354.00
$1,766,455.00 $47,708.00
$15,151.00
$1,989,767.00 $51,406.00
$21,806.00
$1,791,366.00 $45,453.00
$23,455.00
$1,574,468.00 $52,428.00
$23,293.00
$1,402,498.00 $59,573.00
$24,910.00
$992,695.00 $50,824.00
$24,523.00
$2,032,287.00 $37,911.00
$17,064.00
$618,691.00 $49,385.00
$16,298.00
$1,483,891.00 $57,440.00
$24,971.00
$830,502.00 $35,672.00
$26,114.00
$1,311,477.00 $64,644.00
$20,315.00
$2,254,852.00 $59,518.00
$19,364.00
$2,340,777.00 $43,302.00
$15,114.00
$522,921.00 $46,073.00
$16,259.00
$1,780,804.00 $66,295.00
$20,173.00
$1,120,573.00 $49,522.00
$21,510.00
$1,074,914.00 $52,215.00
$20,057.00
$1,996,619.00 $57,151.00
$25,535.00
$2,266,482.00 $64,753.00
$20,773.00
$906,194.00 $55,725.00
$17,606.00
$1,676,862.00 $46,237.00
$26,591.00
$1,253,440.00 $52,632.00
$26,056.00
$1,554,321.00 $59,347.00
$17,655.00
$808,068.00 $59,167.00
$17,267.00
$1,509,685.00 $54,288.00
$23,904.00
$1,893,126.00 $42,282.00
$23,259.00
$1,551,024.00 $48,968.00
$20,045.00
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$1,604,888.00
$793,591.00
$1,025,239.00
$982,462.00
$786,630.00
$1,871,438.00
$849,289.00
$529,624.00
$1,272,403.00
$875,054.00
$2,224,090.00
$2,247,311.00
$1,065,190.00
$2,132,915.00
$2,381,990.00
$1,402,255.00
$1,142,278.00
$1,119,178.00
$2,330,258.00
$1,657,436.00
$2,330,143.00
$2,246,119.00
$1,851,284.00
$1,565,449.00
$631,655.00
$1,041,578.00
$1,717,073.00
$2,086,072.00
$703,115.00
$1,961,968.00
$2,006,155.00
$905,032.00
$1,161,260.00
$1,780,298.00
$1,223,913.00
$1,178,492.00
$1,902,295.00
$1,902,107.00
$1,096,683.00
$2,343,103.00
$1,497,228.00
$2,350,887.00
$1,205,109.00
$1,567,269.00
$1,679,185.00
$1,157,850.00
$704,072.00
$62,180.00
$47,919.00
$46,078.00
$54,289.00
$47,497.00
$46,231.00
$62,353.00
$60,315.00
$66,633.00
$35,083.00
$65,178.00
$36,910.00
$66,059.00
$59,572.00
$59,957.00
$37,839.00
$48,583.00
$59,016.00
$52,865.00
$60,601.00
$42,813.00
$55,714.00
$60,186.00
$52,410.00
$54,838.00
$53,259.00
$49,017.00
$66,546.00
$36,482.00
$56,448.00
$60,244.00
$47,843.00
$62,347.00
$63,689.00
$55,721.00
$52,115.00
$63,008.00
$42,529.00
$54,823.00
$41,489.00
$57,675.00
$56,698.00
$48,343.00
$66,323.00
$38,479.00
$35,737.00
$67,180.00
$25,556.00
$20,679.00
$17,497.00
$26,525.00
$16,240.00
$25,350.00
$19,487.00
$25,323.00
$20,256.00
$18,047.00
$25,494.00
$22,394.00
$21,867.00
$23,295.00
$17,401.00
$24,552.00
$26,322.00
$26,967.00
$17,403.00
$24,307.00
$15,603.00
$24,227.00
$22,651.00
$23,415.00
$23,930.00
$26,069.00
$19,504.00
$15,493.00
$20,155.00
$22,343.00
$21,762.00
$26,314.00
$16,935.00
$19,487.00
$20,090.00
$26,432.00
$18,893.00
$20,260.00
$17,784.00
$22,170.00
$20,074.00
$20,041.00
$16,287.00
$17,635.00
$20,610.00
$19,027.00
$18,978.00
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$746,940.00
$639,623.00
$1,739,492.00
$2,085,389.00
$2,097,363.00
$1,885,468.00
$912,771.00
$1,320,138.00
$1,006,173.00
$1,131,799.00
$2,051,518.00
$1,917,132.00
$904,282.00
$2,126,066.00
$584,061.00
$1,396,500.00
$2,374,813.00
$2,362,562.00
$520,614.00
$2,132,780.00
$2,122,903.00
$1,215,437.00
$980,140.00
$1,372,932.00
$535,332.00
$638,114.00
$1,595,589.00
$1,444,722.00
$1,036,652.00
$926,630.00
$1,239,743.00
$1,203,564.00
$1,188,395.00
$535,153.00
$571,207.00
$2,113,845.00
$2,178,410.00
$518,211.00
$1,484,001.00
$1,217,044.00
$1,158,982.00
$1,720,144.00
$1,809,943.00
$1,928,972.00
$1,768,202.00
$600,007.00
$1,058,409.00
$49,907.00
$44,953.00
$42,005.00
$52,282.00
$51,606.00
$55,151.00
$64,190.00
$43,275.00
$56,647.00
$52,662.00
$36,254.00
$54,716.00
$61,506.00
$54,596.00
$41,359.00
$40,139.00
$51,706.00
$57,447.00
$55,687.00
$37,931.00
$36,422.00
$52,808.00
$41,161.00
$48,869.00
$65,126.00
$53,309.00
$64,271.00
$48,595.00
$66,409.00
$47,080.00
$38,737.00
$43,344.00
$38,236.00
$35,128.00
$51,952.00
$51,209.00
$63,652.00
$44,444.00
$64,194.00
$38,434.00
$62,325.00
$59,895.00
$39,482.00
$54,832.00
$49,814.00
$51,724.00
$52,356.00
$26,886.00
$16,844.00
$16,731.00
$17,566.00
$22,097.00
$21,048.00
$23,957.00
$22,110.00
$17,316.00
$22,443.00
$15,347.00
$21,413.00
$26,971.00
$24,872.00
$21,659.00
$24,211.00
$15,968.00
$25,298.00
$19,039.00
$26,767.00
$26,243.00
$26,666.00
$15,368.00
$24,238.00
$20,365.00
$24,482.00
$24,216.00
$19,994.00
$23,592.00
$25,030.00
$16,336.00
$18,425.00
$22,571.00
$20,766.00
$20,841.00
$26,273.00
$17,950.00
$17,540.00
$21,102.00
$17,498.00
$19,326.00
$19,602.00
$17,654.00
$24,113.00
$25,630.00
$26,255.00
$22,140.00
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$1,309,584.00
$1,557,545.00
$2,127,207.00
$1,307,803.00
$940,162.00
$1,189,299.00
$1,232,238.00
$653,568.00
$886,037.00
$1,455,753.00
$2,226,978.00
$984,515.00
$2,266,842.00
$1,618,531.00
$1,178,062.00
$2,176,119.00
$1,015,840.00
$1,120,681.00
$2,285,149.00
$981,367.00
$1,935,032.00
$1,887,193.00
$1,928,646.00
$641,331.00
$1,392,348.00
$2,130,281.00
$1,756,726.00
$2,234,655.00
$1,118,698.00
$1,358,116.00
$1,591,126.00
$672,442.00
$2,192,122.00
$2,096,579.00
$1,581,675.00
$2,108,277.00
$2,374,076.00
$1,855,329.00
$1,139,544.00
$1,128,138.00
$1,279,604.00
$1,951,778.00
$500,820.00
$2,208,939.00
$1,941,787.00
$1,173,708.00
$1,582,823.00
$35,036.00
$38,405.00
$62,025.00
$61,618.00
$48,877.00
$48,888.00
$62,553.00
$50,330.00
$47,961.00
$39,016.00
$55,705.00
$38,058.00
$54,257.00
$56,013.00
$48,213.00
$60,676.00
$49,962.00
$59,343.00
$67,624.00
$38,992.00
$51,645.00
$49,097.00
$39,325.00
$52,410.00
$57,931.00
$67,810.00
$38,593.00
$48,797.00
$49,742.00
$55,342.00
$47,633.00
$49,880.00
$64,731.00
$43,977.00
$64,872.00
$37,092.00
$59,723.00
$38,693.00
$45,204.00
$53,878.00
$67,236.00
$49,841.00
$66,052.00
$55,689.00
$36,714.00
$43,546.00
$60,454.00
$25,507.00
$24,791.00
$25,038.00
$26,463.00
$17,716.00
$21,443.00
$19,812.00
$17,154.00
$22,580.00
$19,654.00
$15,401.00
$18,496.00
$21,074.00
$21,119.00
$23,355.00
$21,135.00
$17,286.00
$20,638.00
$20,454.00
$15,693.00
$19,588.00
$15,935.00
$24,999.00
$21,971.00
$20,177.00
$17,453.00
$22,934.00
$26,433.00
$15,708.00
$21,572.00
$20,186.00
$21,226.00
$19,826.00
$20,072.00
$18,887.00
$20,615.00
$25,166.00
$22,712.00
$18,991.00
$20,336.00
$24,104.00
$21,658.00
$25,652.00
$20,561.00
$17,384.00
$21,925.00
$25,010.00
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$1,345,436.00
$504,655.00
$636,626.00
$1,048,954.00
$1,408,040.00
$630,388.00
$1,268,879.00
$2,034,640.00
$2,397,435.00
$872,789.00
$2,275,641.00
$1,575,895.00
$2,346,150.00
$2,127,241.00
$2,003,946.00
$1,411,128.00
$2,292,175.00
$2,344,559.00
$806,665.00
$1,851,668.00
$589,250.00
$1,954,455.00
$2,269,304.00
$836,326.00
$789,827.00
$688,472.00
$717,869.00
$1,517,699.00
$986,095.00
$2,002,591.00
$1,380,371.00
$865,326.00
$1,510,176.00
$1,413,854.00
$1,304,132.00
$500,776.00
$2,108,854.00
$1,995,794.00
$975,785.00
$588,132.00
$1,535,614.00
$1,345,328.00
$2,391,056.00
$1,360,610.00
$1,804,798.00
$1,135,208.00
$1,037,096.00
$60,669.00
$53,236.00
$36,153.00
$54,651.00
$63,311.00
$60,524.00
$64,012.00
$51,002.00
$57,743.00
$35,150.00
$42,763.00
$63,386.00
$47,802.00
$43,416.00
$51,226.00
$35,606.00
$48,290.00
$35,410.00
$53,653.00
$38,957.00
$55,469.00
$41,555.00
$37,962.00
$57,286.00
$57,756.00
$50,453.00
$39,495.00
$48,098.00
$60,025.00
$62,820.00
$62,098.00
$47,715.00
$57,973.00
$62,654.00
$35,985.00
$58,818.00
$42,507.00
$57,581.00
$42,971.00
$66,000.00
$66,257.00
$39,054.00
$64,079.00
$61,593.00
$52,386.00
$41,494.00
$43,618.00
$18,835.00
$15,338.00
$15,857.00
$16,436.00
$24,313.00
$22,061.00
$25,377.00
$19,078.00
$18,539.00
$16,091.00
$18,287.00
$20,010.00
$16,929.00
$21,886.00
$18,895.00
$21,006.00
$20,632.00
$25,782.00
$15,132.00
$23,726.00
$26,395.00
$22,787.00
$15,774.00
$19,793.00
$19,363.00
$25,961.00
$22,547.00
$18,494.00
$22,677.00
$20,590.00
$24,215.00
$16,365.00
$23,675.00
$19,920.00
$22,976.00
$21,392.00
$20,803.00
$18,286.00
$15,090.00
$23,250.00
$15,057.00
$25,509.00
$25,080.00
$22,351.00
$24,938.00
$18,310.00
$18,818.00
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$674,215.00
$613,382.00
$1,304,461.00
$2,157,774.00
$1,516,918.00
$1,978,862.00
$948,446.00
$63,406.00
$56,514.00
$40,778.00
$45,558.00
$61,419.00
$37,677.00
$42,712.00
$20,488.00
$19,515.00
$15,141.00
$17,040.00
$26,776.00
$25,844.00
$26,064.00
Chapter 2
Reasoning with Data
© 2019 McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
Learning Objectives
1.
2.
3.
4.
5.
6.
Define reasoning.
Execute deductive reasoning.
Explain an empirically testable conclusion.
Execute inductive reasoning.
Differentiate between deductive and inductive reasoning.
Explain how inductive reasoning can be used to evaluate an
assumption.
7. Describe selection bias in inductive reasoning.
© 2019 McGraw-Hill Education.
2
What is Reasoning?
• Reasoning is the process of forming conclusions, judgments, or
inferences from facts or data
• Reasoning and logic are often used interchangeably
• Logic is a description of the rules and/or steps behind the reasoning
process
© 2019 McGraw-Hill Education.
3
Two Arguments
Argument 1:
• The companies profits are up more than 10% over the past year. An
increase in profits of 10% is the result of excellent management.
You were the manager over the past year. Therefore, I conclude
that you engaged in excellent management last year.
Argument 2:
• Ten of your 300 employees came to me with complaints about your
management. They indicated that you treated them unfairly by not
giving them a raise they deserved. Therefore, I conclude that all of
your employees are disgruntled with your management.
© 2019 McGraw-Hill Education.
4
Understanding Reasoning
• In presenting the two arguments, the goal is not to make a
definitive decision about which you believe (if either)
• The goal is to think about and distinguish different “lines” of
reasoning
• In distinguishing between the different types of reasoning, you
will be able to establish why you believe or question the claims
made in the two arguments
© 2019 McGraw-Hill Education.
5
Two Major Types of Reasoning
Reasoning
Deductive Reasoning
Inductive Reasoning
• Both play an important role in interpreting and drawing
conclusions from data analysis
© 2019 McGraw-Hill Education.
6
Deductive Reasoning
Deductive Reasoning
• Goes from the general to the specific
• Also known as top-down logic
• Seeks to prove statements of the form “If A, then B”
© 2019 McGraw-Hill Education.
7
Deductive Reasoning
• Such reasoning always implies three underlying components:
assumptions (“If A”), methods of proof (“then”), and
conclusions (“B”)
© 2019 McGraw-Hill Education.
8
Deductive Reasoning
• The purest applications of deductive reasoning are in the field of
mathematics
• Two of the most used approaches are direct proofs and
transposition
Direct proofs
• Proof that begins with assumptions, explains methods of proof, and
states the conclusion(s)
Transposition
• Any time a group of assumptions implies a conclusion, then it is
also true that any time the conclusion does not hold, at least one of
the assumptions must not hold
© 2019 McGraw-Hill Education.
9
Direct Proof
• Let’s prove the following statement by direct proof:
If X and Y are odd numbers, then their sum (X + Y) is an even
number
An Example:
If X = 5(odd) and Y = 9(odd), then their sum X + Y = 14 is an even
number
• Failing to find a contradiction is not the same a proving a
statement is generally true
© 2019 McGraw-Hill Education.
10
Direct Proof: A Mathematical Approach
If X and Y are odd numbers, then their sum (X + Y) is an even number
1. X and Y are odd numbers
2. If X is an odd number, then X can be written as X=2K+1, where K is
an integer. (Example: X=13 X=(2 × 6)+1)
3. If Y is an odd number, then Y can be written as Y =2M+1, where M
is an integer, (Example: Y=23 Y=(2 × 11)+1)
4. X+Y=(2K+1)+(2M+1)=2K+2M+2=2(K+M+1)
5. K+M+1 is an integer so X+Y is 2 times an integer
6. Any number that is 2 times an integer is divisible by 2
7. This means X+Y is even
© 2019 McGraw-Hill Education.
11
Direct Proof: Common Sense Approach
“If McDonald’s offers breakfast all day, their revenues will increase.”
1. McDonald’s stores offer breakfast all day.
2. The addition of breakfast during lunch/dinner hours implies more
choices.
3. Customers already choosing McDonald’s during lunch/dinner
hours can continue buying the same meals at McDonald’s.
4. Customers not choosing McDonald’s during lunch/dinner hours
may start eating at McDonald’s.
5. Retaining current customers and adding new ones, McDonald’s
revenues will increase overall.
© 2019 McGraw-Hill Education.
12
Transposition
• While direct proofs are sufficient to prove a point logically, an
alternative approach, transposition, may be more effective
Transposition
• Is the equivalence between the statements “If A, then B” and
“If not B, then A”
• Any time a group of assumptions implies a conclusion, then it
is also true that any time the conclusion does not hold, then at
least one of the assumptions must not hold
© 2019 McGraw-Hill Education.
13
Transposition
• “If A, then B” AND “If not B, then not A”
ASSUMPTIONS
(A)
CONCLUSIONS
(B)
© 2019 McGraw-Hill Education.
14
Transposition: A Mathematical Approach
Prove the statement: If X2 is even, then X is even
1. Suppose X is not an even number; it is instead an odd number
2. If X is an odd number, then X= (2K +1), where K is an integer
3. X2 = (2K+1)2 = 4K2 + 4K+1.
4. 4K2 + 4K = 4(K2 +K) and so is divisible by 2
5. 4K2 + 4K is an even number
6. X2 = 4(K2 +K)+1 is an even number plus 1, meaning it is an odd
number
© 2019 McGraw-Hill Education.
15
Transposition
• The statement was: If X2 is even, then X is even
• Using transposition, the opposite of the conclusion is used to
proof the opposite of the assumption: If X is odd, then X2 is
even would be incorrect
• Transposition can also be used without using mathematics to
prove statements like “If A, then B”.
• Transposition can be particularly effective if an assumption
seems indisputably obvious.
© 2019 McGraw-Hill Education.
16
Transposition: An Example
Proof the statement: “If McDonald’s stores offer breakfast all day,
revenue will increase”
1. McDonald’s stores revenues will not increase
2. This means total revenues from current and new customers will
not increase
3. This means either there will be no new customers or revenues
from current customers will decrease
4. This means there could not have been an expansion in the menu
5. McDonald’s stores do not offer breakfast all day
© 2019 McGraw-Hill Education.
17
Direct Proof and Transposition
Direct Proof
1. State assumptions
2. Explain methods of proof (mathematics, common sense, etc.)
3. State conclusions
Transposition
1. Assume the opposite of the conclusion
2. Explain methods of proof (mathematics, common sense, etc.)
3. State assumption(s) that is (are) violated (not A)
© 2019 McGraw-Hill Education.
18
Deductive Reasoning
• Used commonly in the application of law
• If there is disagreement with a conclusion there are two possible
sources:
1. The method of proof, OR
2. The assumption
• There are two ways of resolving disputes about assumptions
1. Show robustness- the persistent accuracy of a conclusion despite
variation in the associated assumption(s) within the context of a
deductive argument
2. Assess consistency with a collected dataset
© 2019 McGraw-Hill Education.
19
Empirically Testable Conclusions
• An empirically testable conclusion is a conclusion whose validity
can be meaningfully tested using observable data.
Example:
• A banana company’s management staffs are divided into two
groups about their product’s placement in a major grocery store
chain.
• Group 1 believes that change in current location will increase its
sales.
• Group 2 believes that current location is good enough.
© 2019 McGraw-Hill Education.
20
Empirically Testable Conclusions
• Company has the sales data in the current location.
• Company chooses to move its product to a new location and
collects sales data.
• Now the company can meaningfully test the validity of the
management’s competing conclusions.
• Making the actual decision about the validity of an empirically
testable conclusion based on observable data is an application
of inductive reasoning
© 2019 McGraw-Hill Education.
21
Inductive Reasoning
Inductive reasoning
• Reasoning that goes from the specific to the general; bottomup logic
Population
• The entire set of potential observations about which we want
to learn
Data sample
• A subset of population that is collected and observed
© 2019 McGraw-Hill Education.
22
Inductive Reasoning
• Business regularly collect data samples to draw conclusions
about the population after applying inductive reasoning.
• The conclusion from inductive reasoning requires degree of
support (also called inductive probability).
▪ Degree of support is also called the strength of the inductive
argument.
• Example: if we are 50% confident about the conclusion, then
the degree of support is 50%.
© 2019 McGraw-Hill Education.
23
Degrees of Support
Two Types of Degrees of Support
SUBJECTIVE DEGREE OF
SUPPORT
OBJECTIVE DEGREE OF
SUPPORT
(IT IS BASED ON OPINION
AND LACKING STATISTICAL
FOUNDATION)
(IT HAS A STATISTICAL
FOUNDATION AND THUS MORE
CREDIBLE THAN SUBJECTIVE
DEGREE OF SUPPORT)
• Both play an important role in interpreting and drawing
conclusions from data analysis
© 2019 McGraw-Hill Education.
24
Evaluating Assumptions
• Through deductive reasoning, an empirically testable
conclusion is made
• Collect a data sample
• Test the conclusion by comparing the observed outcomes in
the data samples to their corresponding probabilities
• Use inductive reasoning to decide whether the conclusion
passes or fails
▪ If it fails, transposition implies we must reject
▪ If it passes, then we must not reject
© 2019 McGraw-Hill Education.
25
Inductive Reasoning for Evaluating Assumptions
© 2019 McGraw-Hill Education.
26
Selection Bias in Inductive Reasoning
• Improper use of inductive reasoning may lead to inaccurate, or
biased conclusions
• Data-generating process is typically the source of the bias
▪ Survey questions constructed in a leading way
• Confirmation bias is the tendency to confirm a claim
▪ Predictable patterns are discovered
• Predictable-world bias is the tendency to find order when none exists, and
occurs when people “read too much” into perceived patterns from random
data
© …
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