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Solution Manual For Predictive Analytics for Business Strategy , 1st Edition

Struggling with textbook problems? Solution Manual For Predictive Analytics for Business Strategy, 1st Edition offers a clear breakdown of every exercise for easy understanding.

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    1 Chapter 1: The Roles of Data and Predictive Analytics in Business Answers to Questions and Problems 1. a. Structured. The unit of observation is an individual, and for each one, we can identify their: name, age, height, and location clearly. b. Unstructured. There are clearly separate pieces of information being collected (texts, dates, prices) but there isn’t a clear way to assemble them into distinct units of observation. c. Structured. The unit of observation is some sort of rectangular object (it need not have an explicit label for it to be well defined), and the even columns provide information on color, length, weight, and width for each one. d. Unstructured. There are clearly separate pieces of information (time, price, sales) but no clear way to assemble them into distinct units of observation. 2. a. The unit of observation is a store - year. Note that it may be tempting to claim the unit of observation is a store - person - year, since there is also variation in managers. However, as the data are presented, knowing the year and store automatically implies the manager; therefore, the unit of observation is a store - year only. These are panel data. b. The unit of observation is a month. These are time series data. c. The unit of observation is a person - year. These data are a pooled cross - section. d. The unit of observation is a factory. These are cross - sectional data. 3. a. Query. This may seem like pattern discovery, but there needs to be some threshold that qualifies this as a pattern. b. Query. This is simply a request for information for the dataset. c. Causal inference. This describes the causal effect of advertising on sales. d. Pattern discovery. This is a form of outlier detection. e. Pattern discovery . This is a form of association analysis.

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    2 4. L ead information pertains to what will happen and lag information pertains to what did happen. 5. Passive prediction involves predicting outcomes while observing, but not altering, their determining factors. Active prediction involves predicting outcom es after altering at least one o f their determining factors. 6. a. Active prediction – Tom exogenously alters his diet. b. Passive prediction – Ann does not directly alter the number of visits to her site. c. Active prediction – Laura exogenously alters her advertising. d. Passive prediction – Alex does not directly alter people’s credit card purchasing. e. Passive prediction – John does not directly alter the voter’s answers. 7. As stated in the text, it allows the decision - maker to make evidence - based assessments of expected outcomes from alternative strategies, and then choose the optimal one based on her business objective. 8. a. i. A theoretical refute may be as simple as follows. Based on your own sense of the matter, people find the ads entertaining, but not enough to substantially respond in terms of purchasing. Therefore, the change in sales will not be enough to offset the costs of the ads, meaning increased ad expenditure will lower profits. ii. You collect data on varying levels of ad expend iture along with profits across locations and/or time. Then, using techniques described in later chapters, you analyze how profits respond to changes in ad expenditure in the data. If the analysis shows profits declining with increases in ad expenditure, this would constitute a refutation to the claim. b. Data consist of what actually occurred, allowing for evidence - based decision - making, rather than “gut” - based decision - making. 9. Here, we need three factors that we believe have a causal effect on the number of years an employee stays with a firm. Three such factors might be: 1. Education (which might influence the employee’s competing options)

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    3 2. Number of nearby rival firms (also may influence the employee’s competing options) 3. Age when hired ( which may be indicative of the employee’s job mobility) 10. Following the example in the text, we can formally express the data generating process for weekly soda sales as: 𝑆𝑎𝑙𝑒𝑠 𝑡 = 𝑓 ( 𝑃𝑟𝑖𝑐𝑒 𝑡 , 𝑃𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑡 , 𝐻𝑜𝑙𝑖𝑑𝑎𝑦 𝑡 ) + 𝑈 𝑡 . 11. a. This does not require active prediction. Rather, it is a good example of an application of passive prediction. We want to predict how purchases relate to age, and we are not making changes to our customers’ ages. b. This does require active prediction. We are considering making an active change in strategy – in the form of a new celebrity endorsement – and we want to predict how sales will respond. c. This does require active prediction. We are actively changing product placement (a strategic move), and want to know the impact on profits. 12. Amanda is making the active prediction. She is determining what will happen with a change in strategy (i.e., a price cut). In comparison, Darryl is making a passive prediction. He is using demographics – which Meredith is not considering, or capable of, changing – to predict the likelihood of an accident. 13. See DataLoad .xlsx for the data loading, or the table below provides an example. The unit of observation is a person - year. The data are panel data.

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    4 14. (a,b,c): See Scorecard Answer.xlsx 15. a. i. $1,468,424.42 ii. 11,526,750.78 iii. 3,579,884.506 iv. $51,439.46 v. $353,890,286.00 b. Two candidates incl ude mean of Materials Costs ($21 , 161 . 41 ) and Variance of Labor Costs ( $87,892,572 ). 16. a. $1,481,100.02 b. $504,655 c. Region 166 d. Region 223 e. $2,397,435 - $500,776 = $1,896,659 17. a. There is a strong positive correlation between a customer being active and their age level. Hence, it appears younger customers are most likely to drop. This is lead information since it is designed to look ahead and assess where the greatest risks of customer loss will be in the future. b. The North R egion had the most customers (84 ). This is lag information, since it is simply reporting what happened.

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    1 Chapter 2 : Reasoning with Data Answers to Questions and Problems 1. Reasoning is the process of forming conclusions, judgments, or inferences from facts or premises. 2. a. Inductive reasoning. You are starting with a specific observation and ending with a general conclusion. b. Deductive reasoning. You are starting with an assumption and ending with a conclusion. c. Ded uctive reasoning. You are starting with an assumption and ending with a conclusion. d. Inductive reasoning. You are starting with a specific observation and ending with a general conclusion. 3. a. If a demand curve is downward sloping, then quantity demanded is always declining with increases in price by definition. A change in price from $20 to $25 is a price increase, and so must result in a decline in quantity demanded. Since quantity demanded was 4,000 before the price increase, it must be less than 4,000 after the price increase. b. Suppose increasing price from $20 to $25 resulted in sales at least as high as 4,000. Then, this represents a price increase where quantity demanded did not fall. This means that the demand curve is not downward sloping, at least across these price points; hence, demand canno t be generally characterized as downward - sloping. 4. There is one definitive problem with this argument: T here is no basis for the degree of support being 1%. In other words, this is a subjective degree of support. An additional possible problem is that the results from early polling may be a selected sample consisting of people relatively in favor of, or against, a candidate compared to the mean overall. This would potentially invalidate any conclusions that are based on an assumption of a random sample.

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    2 5. Reasoning provides the framework that allows all involved to clearly see how to go from a dataset to a meaningful conclusion. Reasoning allows for a rigorous argument, in contrast to using instincts or feelings. 6. a. This is neither a direct proof nor transposition. Here, we are trying to prove the statement by claiming “If B, then A,” where B is “our margins will increase” and A is “we target our advertising to a younger audience.” Showing B implies A does not necessarily mean A implies B, so this is not a valid proof. b. This is transposition. Here, we are assuming the opposite of the conclusion and showing the assumption cannot hold. c. This is a direct proof. We start with the assumption and move directly to the conclusion. 7. a. Transposition. By walking backward from assuming the conclusion is not true, we are forced to think through the set of assumptions that might consequently be refuted. b. One simple hidden assumption is that the targeted advertising is effective for a younger audience. If the younger audience does not respond to the targeted advertising, the proof breaks down. 8. An empirically testable conclusion resulting from your friend being a faster sprinter is that your friend would defeat you in a sprinting race. You could then test this conclusion by actually running the race and see who wins. 9. These data likely suffer from both collector selection bias and member selection bias. For collector selection bias, the people in the data being collected are those that the manager has not let go from the firm; hence, there is selection in terms of which employees the manager allows to stay. For member selection bias, the employees in the data are those who chose to stay with the firm and not go work somewhere else. Both types of selection, which are likely present in these data, could lead to biased conclusions about the average monthly sales for new hires in general. 10. A subjective degree of support is based on opinion and does not have a statistical foundation. In contrast, an objective degree of support does have a statistical foundation. Hence, the objective degree of support is grounded in an associated statistical model that generates concrete figures capturing the level of certainty.

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    3 11. a. Inductive reasoning. b. Deductive reasoning. c. Inductive reasoning. 12. a. This is empirically testable. You can have the teams play any number of times, and compare the proportion of wins for Team A to 65%. b. This is not em pirically testable. Bruce Lee did not compete in the 1970 tournament, and we cannot go back to observe his performance if he had. Hence, there are no observations currently available, or possible to collect, that could evaluate this conclusion. c. This is empirically testable. You can observe profits at each store next year, and compare the proportion of stores that had increased profits to 75%. 13. Observe the car salesman’s number of sales for the next five customers in the store. If he makes no sales, you could inductively reason that he does not in fact have a 50% success rate in general. 14. a. The empirically testable conclusion consists of the probabilities in the table. For example, if your assumption holds, the probability of 8 correct picks is 4.4%. b. You could test this conclusion by comparing the number of correct picks the broker makes against the probabilities. In particular, if you observed a very high (e.g., 9 or 10) or very low (e.g., 0 or 1) number of correct picks, you may question whether this conclusion is accurate. c. The line of reasoning is as follows. First, using deductive reasoning, we go from the assumption of a 50% likelihood of success to the probability table in the problem , which is the empirically testable conclusion . Next, using inductive reasoning, we observe the number of correct picks and decide whether or not to reject the probability table as being true. Last, if we decide to reject the probability table, we use deductive reasoning (in the form of transposition) to reject the assumption of a 50% likelihood of success. 15. One possible source of selection bias is via collector selection bias. The broker may have sent you picks for stocks for which she had some inside knowledge , and she may not generally possess this type of knowledge when making picks. Another possible source of selection bias is member selection bias. A clever scam artist would simply make all 2 10 possible combinations of stock picks and send e ach different set

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    4 of picks to 2 10 different people. Then, the picks you receive is a selection of one set of picks out of the 2 10 that were actually made. You are then basing your reasoning on the one set of picks you observed, and not the full sample of picks that were made.

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    1 Chapter 3 : Reasoning from Sample to Population Answers to Questions and Problems 1. a. The sample mean is the sum of all 16 numbe rs divided by 16, which is 24.06 . b. The sample standard deviation is the square root of the sample variance. The sample variance is 1 𝑁 − 1 ∑ ( 𝑥 𝑖 − 𝑋 ) 2 𝑁 𝑖 = 1 = 1 15 ∑ ( 𝑥 𝑖 − 24 . 06 ) 2 16 𝑖 = 1 = 166 . 46 . Therefore, the sample standard deviation is 12.90 . c. They are estimators for the population mean and population standard deviation, respectively. d. An unbiased estimator, informally, is a “reasonable guess” for its corresponding population parameter. More formally, an unbiased estimator is one where its expected value is equal to its corresponding population parameter. 2. You potentially have a non - random sample, since only a subset of the 1,000 customers you sampled gave you a response. This sample may consist of people more willing to reveal their income, and it’s reasonable to think this group may tend to be those who have a good income. In that case, the sample mean will be a biased estimate of the population mean (in this case, likely biased upward), and the confidence interval will span numbers that are too high. 3. a. The 90% confidence interval for the click through rate is 0 . 12 ± 1 . 65 ( 0 . 325 √ 2271 ) . Rounding to the nearest thousandth, we have a 90% confidence interval of (0.109,0.131 ). b. This confidence interval means that we are 90% confident that the population - level cl ick through rate is between 0.109 and 0.13 1 . Put another way, if we took many samples and constructed the confidence interval the same way as we did for part a each time, 90% of those intervals would capture the population - level click through rate. c. This would mean our assumption of a sample size over 30 is no longer correct. This doesn’t mean our confidence interval is necessarily wrong; however, the confidence level we place on it depends on our ability to apply the central limit theorem, which we can no longer do. 4. a. The t - stat is (0.07 - 0.075)/(0.256/sqrt(341)) = - 0.361.

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    2 b. The t - stat is the test statistic corresponding to the sample mean which is then used to conduct hypothesis tests. c. The p - value for this t - stat is 0.719. d. The p - value is the probability of observing a draw from a t - distribution that is at least as extreme (far from zero) as the t - stat we observed. 5. See the graph below for the answers to a & b 6. a. The 95% confidence interval will be wider. To construct it, you take 1.96 standard deviations in each direction, as opposed to 1.65 standard deviations. Conceptually, this makes sense as well – you need the confidence interval to include more values in order to have a higher level of confidence that it contains the population parameter. b. A 100% confidence interval is the entire real line. Conceptually, in order to be 100% confident that the confidence interval contains the population parameter, we have to allow for all possible values. 7. a. Note that 26.2 is the sample mean. Also, recall that the p - value in this case is the probability of seeing a number at least as extreme as the sample mean when the null is true. Since the sample mean is equal to the hypothesized population mean, every number is at least as extreme as what we saw (we can’t get less extreme than seeing the population mean!). Therefore, the p - value is 1.0, or 100%. p - value 20 26.2 13.8 𝑋

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    3 b. No. With a p - value of 1.0, we would never reject this null, no matter the degree of support we choose. This is sensible, since there is no basis for rejecting the hypothesized population mean if the sample mean exactly equals it. 8. Following Reasoning Box 3 - 5, deductive reasoning plays a role in two places. First, it plays a role in the final prediction. Assuming the causal relationship between price and revenues is about $207,500 per $1 increase (taking the mid - point of the confidence interval), it is immediate to conclude what a $2 increase in price will do. Second, it plays a role in establishing the causality between price and revenue and the distribution of an estimator for the magnitude of this causal relationship in the population. Specifically, we must make assumptions that imply both causality and the distribution of our estimator for the effect of price on revenue. 9. Refer to the Soda_Answer.xlsx file. a. This is the null hypothesis. b. Using the sample mean, sample standard deviation, and sample size, the t - stat is (2.69 – 2.58) / (0.439 / sqrt(35)) = 1.547. c. The p - value is 0.131. d. The t - stat is less than 1. 6 5, so we fail to reject the null with 90% confidence. e. The p - value is more than 0.10, so we fail to reject the null with 90% confidence. f. No. The values for the t - stat that lead to rejection using 90% confidence exactly correspond to the values for the t - stat that would generate a p - value of less than 0.10. 10. Refer to the WebVisits _Answer.xlsx file. a. Using the data, calculate the sample standard deviation and divide by the square root of the number of observations, yielding approximately 0.043. Then, take the mean duration (approximately 8.504), and add and subtract 1.65 × 0.043 to get the confidence interval. Hence, t he 9 0% confidence interval is (8.433,8.575 ). b. Using the data, calculate the sample standard deviation and divide by the square root of the number of observations, yielding approximately 0.043. Then, take the mean duration (approximately 8.504), and add and subtract 1.96 × 0.043 to get the confidence interval. Hence, t he 95% confidence interval is ( 8.419,8.588 ).

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    4 c. Using the data, calculate the sample standard deviation and divide by the square root of the number of observations, yielding approximately 0.043. Then, take the mean duration (approximately 8.504), and add and subtract 2.58 × 0.043 to get the confidence interval. Hence, th e 99% confidence interval is (8.392,8.615 ). d. A possible issue with these confidence intervals is that the sample data may not be a random sample. The question is whether there is anything “special” about the month during which you collected the data. For example, if there is greater visit intensity during the Holiday Season, then using the month of December may generate a sample mean that is not an unbiased estimator of the population mean. 11. Refer to the WebProfits _Answer.xlsx file. a. The 9 9% confidence interval is (8.898,9.813 ) . b. i. The t - stat is - 12.08. ii. The p - value is 3.95 x 10 - 33 – an extremely small number. iii. The p - value is far less than 0.05, so reject 11.5 as the mean profit per visit for all visits. iv. If we assume the sample data is a random sample from the population, and given the sample size is large (easily more than 30), we can use the sample mean, sample standard deviation and sample size to calculate the t - stat. The p - value is the probability we would observe a t - stat at least as large (in absolute value) as the one we did observe, given the mean profit per visit in the population were $11.50. Since this is less than 0.05, we reject the claim that the population mean profit per visit is $11.50. 12. Refer to the WebProfits _Answer.xlsx file. a. T he t - stat requires us to calculate the mean of Profit (approximately 9.356) and the sample standard deviation (approximately 12.215). Then, the t - stat is (9.356 – 9) / (12.215 / sqrt (4738)) = 2.004. b. To get the area in the tails of a standard normal distribution (above 2.004 and below - 2.004), we use (1 - 2 × norm.s.dist(2.004,true)) in Excel. The p - value is 0.045. c. Since the confidence level is 99%, we compare the p - value to 0.01 (1 – 99/100). Here, the p - value is more than 0.01, so we fail to reject the null hypothesis. This means we cannot reject that the mean profit per visit for all visitors is $9.00.

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    5 d. If we assume the sample data is a random sample from the population, and given the sample size is large (easily more than 30), we can use the sample mean, sample standard deviation and sample size to calculate the t - stat. The p - value is the probability we would observe a t - stat at least as large (in absolute value) as the one we did observe, given the mean profit per visit in the population were $9.0 0. Since this is more than 0.01 , we fail to reject the claim that the populatio n mean profit per visit is $9.0 0.

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    1 Chapter 4 : The Scientific Method: The Gold Standard for Establishing Causality Answers to Questions and Problems 1. Option c) Collect market data. As we’ve seen in the chapter, market data per se is not well suited for the scientific method, since it rarely is generated via a controlled experiment. 2. A correct answer here will have components comparable to those for the business example in the text. A brief outline is as follows: Step 2 ( Do background research): Learn more about the posed question, e.g., by running consumer surveys. Step 3 (Formulate a hypothesis): Propose what the relationship between the variables is, e.g., an increase in X decreases Y. Step 4 (Run an experiment): Randomly assign different values of X and observe how the corresponding values of Y. Step 5 (Analyze the data and draw conclusions): Build confidence intervals and/or conduct a hypothesis test designed to evaluate your hypothesis, and draw conclusions as to whether the data support the hypothesis or not. Step 6 (Communicate the findings): Explain the methodology and findings from your experiment. 3. The effect of the treatment on the treated is the expected change in the outcome from receiving the treatment for the group of participants actually receiving the treatment. The average treatment effect is the expected change in the outcome from receiving the treatment for the entire population, regardless of their actual treatment status. 4. a. The flaw is that the two days for which she observed price and profits are not identical to the day for which she wants to measure the effect of a price change (i.e., treatment effect). Put another way, she would like to know Profits i T – Profits i NT , but instead has Profits j T – Profits k NT , where i stands for her store tomorrow, and j and k stand for her store on the two days where she observed price and profits.

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    2 b. She would like to observe profits tomorrow when price is unchanged (Profits i NT ), and then go back and observe profits on the exact same day when price is 10% higher (Profits i T ), and then take the difference. Of course, it is not possible to do this. 5. a. This is not an example of zero selection bias. Rather, this is an example of a differential treatment effect across subgroups of the population. b. This is an example of zero selection bias. Mondays and Wednesdays have the same expected outcome when receiving no treatment. c. This is not an example of zero selection bias. This just states that the average outcome is the same for the treated and untreated. 6. a. This is an example of ETT ≠ ATE. Those receiving the coupon respond differently to it than the general population. b. This is not an example of ETT ≠ ATE. Rather, this is an example of a nonzero selection bias. c. This is not an example of ETT ≠ ATE. Rather, this is an example of zero selection bias. 7. Non - experimental data almost always involve a non - randomly assigned treatment. If the treatment is instead assigned in a way that those receiving the treatment are different than those who don’t (e.g., because they respond differently and/or have different expected outcomes with no treatment), then we will get a biased estimate of the treatment effect using standard techniques. 8. Managers generally are not making strategic decisions randomly, but optimally, often to maximize profits. For example, they may tend to make strategic decisions so that treatments (e.g., price discounts) are assigned where they will be most profitable (ETT > ATE), or possibly in markets that currently have the least profits (Selection Bias < 0). 9. Yes, it implies there is selection bias, and it is greater than zero. That is, firms that received the treatment (Google advertising) have higher sales than firms not receiving the treatment in the case where neither group gets the treatment. Hence, the selected treatment assignment is precluding us from measuring the ATE by simply comparing the average sales for the treated to the average sales for the untreated.

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