, SOLUTION MANUAL FOR Business Analytics
Applied Modelling and Prediction by James Abdey
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, Business Analytics:
Applied Modelling and Prediction
Solutions to end-of-chapter exercises
Chapter 1:
Decision-making under uncertainty
,ii
,Chapter 1
Decision-making under uncertainty
1.1 Exercises
1.1.1 Test your understanding
1. What is meant by ‘uncertainty’ ?
Solution:
Uncertainty refers to a lack of knowledge, information or predictability about a particular situation,
event or outcome. It signifies a state of doubt or ambiguity where the future or the true nature of
something is uncertain. Uncertainty can arise from various factors, such as incomplete data,
conflicting evidence, complexity, or the presence of unpredictable variables. It often poses challenges
in decision-making, planning, and risk assessment as it hampers our ability to accurately foresee or
quantify potential outcomes. Managing uncertainty involves acknowledging its presence, assessing
probabilities, considering alternative scenarios, and adopting flexible approaches to adapt to
changing circumstances.
2. What is the difference between ‘dependent’ and ‘independent’ variables?
Solution:
A dependent variable is the variable being measured or observed in an experiment or study. It is the
outcome or result in which we are interested in understanding, explaining or predicting. Examples
of dependent variables in business analytics include:
• behavioural responses, such as customer awareness, brand perception, knowledge, intention to
purchase and preference.
• performance metrics, such as sales revenues, production costs, profits, market share, cash-flow
and share price.
Independent variables are those that impact the dependent variable – think of it in terms of ‘cause
and effect’. Examples of independent variables in business analytics include:
• marketing mix variables, such as product, price, placement and promotion (the 4 Ps), which
are controllable, i.e. are under the control of the decision-maker.
• situational factors, such as demand, competition, economic climate, political climate, exchange
rates, supply chain, regulations and technology, which are uncontrollable, i.e. are not under the
control of the decision-maker.
The relationship between the dependent and independent variables is often explored through
statistical analysis to determine whether changes in the independent variable cause changes in the
dependent variable. This helps establish cause-and-effect relationships and provides insights into the
phenomenon under investigation. Understanding the distinction between dependent and
1
,1. Decision-making under uncertainty
independent variables is fundamental for designing experiments, conducting research, and drawing
meaningful conclusions from data.
3. Identify examples of real-world dependent variables for any business problem of your choice.
Solution:
Consider a hotel. Management may be interested in the following dependent variables.
• Customer satisfaction score – this could be measured using surveys or feedback forms where
customers rate their overall satisfaction with the hotel, its services, staff, amenities, cleanliness,
etc. The satisfaction score can be a numerical rating or a categorical measure (for example,
ranging from ‘very satisfied’ to ‘ very dissatisfied’).
• Revenue per customer – this variable represents the average amount of money a customer
spends during their stay. Higher revenue per customer can indicate customer satisfaction, as
satisfied guests are more likely to use additional services, such as room upgrades, spa
treatments, or dining options.
• Customer retention rate – this metric indicates the percentage of customers who continue to
stay at the hotel over a specific period of time. It reflects customer satisfaction and loyalty, as
satisfied customers are more likely to return in the future!
4. For each dependent variable identified in Question 3, what are the likely independent variables?
Briefly justify your choice.
Solution:
Customer satisfaction score would likely depend on the following:
• Service quality.
• Price/value for money.
• Food and beverage quality.
• Room cleanliness.
• Location.
• Facilities.
Revenue per customer would likely depend on the following:
• Room type booked.
• Length of stay.
• Season of the booking (peak vs. off-peak).
• Ancillary services used.
• In-room dining.
• Purpose of visit (business vs. leisure).
Customer retention rate would likely depend on the following:
• Service quality (note also for customer satisfaction score!).
• Price/value for money (note also for customer satisfaction score!).
• Loyalty programs (accrue points for free nights, perhaps).
2
, 1.1. Exercises
• Special packages (think conferences, weddings etc.).
• Brand image.
• Partnership with other hotel brands.
Note the above are not necessarily collectively exhaustive lists!
5. What is meant by the ‘four Ps’ ?
Solution:
The ‘four Ps’ are known as the marketing mix variables:
• Product – what the business is selling (which could be a tangible good, or intangible service).
• Price – what price to sell at and whether to offer a discount.
• Placement – the provision of customer access and convenience.
• Promotion – the choice of marketing communications.
6. Explain the DIKW pyramid.
Solution:
The pyramid models the conversion of (i) data, into (ii) information, from which we gain (iii)
knowledge, leading to our enlightenment with (iv) wisdom. The pyramid illustrates these as
hierarchical relationships.
7. What is a model?
Solution:
A model is a deliberate simplification of reality.
A good model retains the most important features of reality and ignores less important details.
Immediately we see that we face a trade-off. The benefit of a model is that we simplify the complex
real world. The cost of a model is that by simplifying reality we engineer a departure from reality.
Broadly speaking, we would be happy if the benefit exceeded the cost, i.e. if the simplicity made it
easier for us to understand and analyse the real world while incurring only a minimal departure
from reality.
8. For a city other than London with a metro system, look at the official map of the network. Critique
the map, noting any possible improvements you would recommend are made.
Solution:
Possible improvements may relate to:
• geographic accuracy
• clarity of presentation
• ease of navigation.
3
, 1. Decision-making under uncertainty
9. A friend of yours is a contestant on the Monty Hall game show. Your friend tells you ‘No matter
what, I will not switch door’. Would you support your friend’s decision (to maintain your
friendship!) or would you advise otherwise?
Solution:
At the risk of jeopardising your friendship, you should (politely) point out that probabilistically it is
optimal to switch door. Of course, you need to balance this with the possibility that the original
door chosen is the correct door, in which case you may never be forgiven if your friend followed your
advice!
10. Suppose the producers of the Monty Hall show changed the format of the game. Instead of there
being three doors, there are now n > 3 doors. The contestant chooses a door. Monty (who continues
to know where the car is) opens n − 2 doors, leaving the contestant’s original door and one other
door unopened.
(a) In terms of ‘to switch, or not to switch?’ what would you recommend is the optimal strategy
and why?
(b) Do you support the producers in increasing the number of doors to n > 3? Justify your view.
Solution:
(a) With n > 3 doors, the probability that the correct door is chosen at the start by the contestant
is 1/n. Hence the probability that the correct door is one of the other n − 1 doors is (n − 1)/n,
and clearly:
1 n−1
< .
n n
Once Monty opens n − 2 doors (excluding the contestant’s original choice, of course), the
probability of winning by switching is (n − 1)/n since this amount of probability is ‘inherited’
by the one door Monty chooses not to open. Decision-making under uncertainty requires us to
‘play to the probabilities’, hence it is optimal to switch.
Chapter 4 solves the Monty Hall problem more formally using Bayes’ theorem.
(b) If contestants are savvy enough to understand the probabilistic argument for switching door
each time, then we would expect all such contestants to switch. This would mean that (in
percentage terms) the win rate of contestants (and hence the loss rate of the show’s producers)
in the long run would be:
n−1
× 100%.
n
As n increases, this worsens the situation for the show’s producers (more prizes are won, which
costs money!) so increasing the number of doors would seem to be a bad idea. Also, television
shows are meant to be for entertainment, so with n = 3 doors this maximises the extent of
unpredictability about whether the contestant would win, which in turn would likely be
optimal for audience viewing figures. Suspense is more exciting!
1.1.2 Case study corner
For a company or industry of your choice, formulate a possible quantitative business problem which
could be analysed. In particular, think about the following.
What is the specific business question to be addressed?
4
, 1.1. Exercises
What are the business objectives of the analysis?
What are the dependent and independent variables?
Are there any challenges in collecting relevant data to analyse the problem?
Are there any uncertainties involved with the business problem? If so, what are they?
Solution:
Formulating a problem suitable for quantitative analysis begins with posing a question. Suppose the
company’s question is: ‘What price should we set for our new product?’
While we may have previously relied on gut instinct decisions, we now aim to approach this question
using a more quantitative approach. To answer it, we must identify the factors which may influence the
pricing decision. The challenge lies in the lack of knowledge regarding consumers’ willingness to pay.
However, we would likely have data on manufacturing costs and marketing expenses for our product (or
at least reasonable estimates).
Market research could be conducted to examine the current market landscape and the pricing strategies
adopted by competitors for similar products. Such research encompasses various approaches, each with
its own set of assumptions and uncertainties. By analysing this market research, we could estimate what
consumers might be willing to pay for a similar product and develop a pricing structure accordingly.
However, there are additional uncertainties that need to be considered. For instance:
Will there still be demand for our product when it is launched?
Will consumers have the financial means to purchase it at that time? (If there was a recession,
consumers may reduce their discretionary spending.)
Even if we price our product lower than our competitor(s), will consumers remain loyal to their
familiar brand and refrain from purchasing our product?
To address these uncertainties, we could conduct surveys to collect data on brand loyalty, make
predictions regarding consumers’ future willingness to pay, and assume that demand for our product will
be strong at launch. By gathering relevant data related to these uncertainties and incorporating logical
assumptions, we can create data-driven models to predict the outcomes of our proposed pricing
structures.
5
, Business Analytics:
Applied Modelling and Prediction
Solutions to end-of-chapter exercises
Chapter 2:
Descriptive statistics
Applied Modelling and Prediction by James Abdey
Notes
1- The file is chapter after chapter.
2- We have shown you few pages sample.
3- The file contains all Appendix and Excel sheet
if it exists.
4- We have all what you need, we make update
at every time. There are many new editions
waiting you.
5- If you think you purchased the wrong file You
can contact us at every time, we can replace it
with true one.
Our email:
, Business Analytics:
Applied Modelling and Prediction
Solutions to end-of-chapter exercises
Chapter 1:
Decision-making under uncertainty
,ii
,Chapter 1
Decision-making under uncertainty
1.1 Exercises
1.1.1 Test your understanding
1. What is meant by ‘uncertainty’ ?
Solution:
Uncertainty refers to a lack of knowledge, information or predictability about a particular situation,
event or outcome. It signifies a state of doubt or ambiguity where the future or the true nature of
something is uncertain. Uncertainty can arise from various factors, such as incomplete data,
conflicting evidence, complexity, or the presence of unpredictable variables. It often poses challenges
in decision-making, planning, and risk assessment as it hampers our ability to accurately foresee or
quantify potential outcomes. Managing uncertainty involves acknowledging its presence, assessing
probabilities, considering alternative scenarios, and adopting flexible approaches to adapt to
changing circumstances.
2. What is the difference between ‘dependent’ and ‘independent’ variables?
Solution:
A dependent variable is the variable being measured or observed in an experiment or study. It is the
outcome or result in which we are interested in understanding, explaining or predicting. Examples
of dependent variables in business analytics include:
• behavioural responses, such as customer awareness, brand perception, knowledge, intention to
purchase and preference.
• performance metrics, such as sales revenues, production costs, profits, market share, cash-flow
and share price.
Independent variables are those that impact the dependent variable – think of it in terms of ‘cause
and effect’. Examples of independent variables in business analytics include:
• marketing mix variables, such as product, price, placement and promotion (the 4 Ps), which
are controllable, i.e. are under the control of the decision-maker.
• situational factors, such as demand, competition, economic climate, political climate, exchange
rates, supply chain, regulations and technology, which are uncontrollable, i.e. are not under the
control of the decision-maker.
The relationship between the dependent and independent variables is often explored through
statistical analysis to determine whether changes in the independent variable cause changes in the
dependent variable. This helps establish cause-and-effect relationships and provides insights into the
phenomenon under investigation. Understanding the distinction between dependent and
1
,1. Decision-making under uncertainty
independent variables is fundamental for designing experiments, conducting research, and drawing
meaningful conclusions from data.
3. Identify examples of real-world dependent variables for any business problem of your choice.
Solution:
Consider a hotel. Management may be interested in the following dependent variables.
• Customer satisfaction score – this could be measured using surveys or feedback forms where
customers rate their overall satisfaction with the hotel, its services, staff, amenities, cleanliness,
etc. The satisfaction score can be a numerical rating or a categorical measure (for example,
ranging from ‘very satisfied’ to ‘ very dissatisfied’).
• Revenue per customer – this variable represents the average amount of money a customer
spends during their stay. Higher revenue per customer can indicate customer satisfaction, as
satisfied guests are more likely to use additional services, such as room upgrades, spa
treatments, or dining options.
• Customer retention rate – this metric indicates the percentage of customers who continue to
stay at the hotel over a specific period of time. It reflects customer satisfaction and loyalty, as
satisfied customers are more likely to return in the future!
4. For each dependent variable identified in Question 3, what are the likely independent variables?
Briefly justify your choice.
Solution:
Customer satisfaction score would likely depend on the following:
• Service quality.
• Price/value for money.
• Food and beverage quality.
• Room cleanliness.
• Location.
• Facilities.
Revenue per customer would likely depend on the following:
• Room type booked.
• Length of stay.
• Season of the booking (peak vs. off-peak).
• Ancillary services used.
• In-room dining.
• Purpose of visit (business vs. leisure).
Customer retention rate would likely depend on the following:
• Service quality (note also for customer satisfaction score!).
• Price/value for money (note also for customer satisfaction score!).
• Loyalty programs (accrue points for free nights, perhaps).
2
, 1.1. Exercises
• Special packages (think conferences, weddings etc.).
• Brand image.
• Partnership with other hotel brands.
Note the above are not necessarily collectively exhaustive lists!
5. What is meant by the ‘four Ps’ ?
Solution:
The ‘four Ps’ are known as the marketing mix variables:
• Product – what the business is selling (which could be a tangible good, or intangible service).
• Price – what price to sell at and whether to offer a discount.
• Placement – the provision of customer access and convenience.
• Promotion – the choice of marketing communications.
6. Explain the DIKW pyramid.
Solution:
The pyramid models the conversion of (i) data, into (ii) information, from which we gain (iii)
knowledge, leading to our enlightenment with (iv) wisdom. The pyramid illustrates these as
hierarchical relationships.
7. What is a model?
Solution:
A model is a deliberate simplification of reality.
A good model retains the most important features of reality and ignores less important details.
Immediately we see that we face a trade-off. The benefit of a model is that we simplify the complex
real world. The cost of a model is that by simplifying reality we engineer a departure from reality.
Broadly speaking, we would be happy if the benefit exceeded the cost, i.e. if the simplicity made it
easier for us to understand and analyse the real world while incurring only a minimal departure
from reality.
8. For a city other than London with a metro system, look at the official map of the network. Critique
the map, noting any possible improvements you would recommend are made.
Solution:
Possible improvements may relate to:
• geographic accuracy
• clarity of presentation
• ease of navigation.
3
, 1. Decision-making under uncertainty
9. A friend of yours is a contestant on the Monty Hall game show. Your friend tells you ‘No matter
what, I will not switch door’. Would you support your friend’s decision (to maintain your
friendship!) or would you advise otherwise?
Solution:
At the risk of jeopardising your friendship, you should (politely) point out that probabilistically it is
optimal to switch door. Of course, you need to balance this with the possibility that the original
door chosen is the correct door, in which case you may never be forgiven if your friend followed your
advice!
10. Suppose the producers of the Monty Hall show changed the format of the game. Instead of there
being three doors, there are now n > 3 doors. The contestant chooses a door. Monty (who continues
to know where the car is) opens n − 2 doors, leaving the contestant’s original door and one other
door unopened.
(a) In terms of ‘to switch, or not to switch?’ what would you recommend is the optimal strategy
and why?
(b) Do you support the producers in increasing the number of doors to n > 3? Justify your view.
Solution:
(a) With n > 3 doors, the probability that the correct door is chosen at the start by the contestant
is 1/n. Hence the probability that the correct door is one of the other n − 1 doors is (n − 1)/n,
and clearly:
1 n−1
< .
n n
Once Monty opens n − 2 doors (excluding the contestant’s original choice, of course), the
probability of winning by switching is (n − 1)/n since this amount of probability is ‘inherited’
by the one door Monty chooses not to open. Decision-making under uncertainty requires us to
‘play to the probabilities’, hence it is optimal to switch.
Chapter 4 solves the Monty Hall problem more formally using Bayes’ theorem.
(b) If contestants are savvy enough to understand the probabilistic argument for switching door
each time, then we would expect all such contestants to switch. This would mean that (in
percentage terms) the win rate of contestants (and hence the loss rate of the show’s producers)
in the long run would be:
n−1
× 100%.
n
As n increases, this worsens the situation for the show’s producers (more prizes are won, which
costs money!) so increasing the number of doors would seem to be a bad idea. Also, television
shows are meant to be for entertainment, so with n = 3 doors this maximises the extent of
unpredictability about whether the contestant would win, which in turn would likely be
optimal for audience viewing figures. Suspense is more exciting!
1.1.2 Case study corner
For a company or industry of your choice, formulate a possible quantitative business problem which
could be analysed. In particular, think about the following.
What is the specific business question to be addressed?
4
, 1.1. Exercises
What are the business objectives of the analysis?
What are the dependent and independent variables?
Are there any challenges in collecting relevant data to analyse the problem?
Are there any uncertainties involved with the business problem? If so, what are they?
Solution:
Formulating a problem suitable for quantitative analysis begins with posing a question. Suppose the
company’s question is: ‘What price should we set for our new product?’
While we may have previously relied on gut instinct decisions, we now aim to approach this question
using a more quantitative approach. To answer it, we must identify the factors which may influence the
pricing decision. The challenge lies in the lack of knowledge regarding consumers’ willingness to pay.
However, we would likely have data on manufacturing costs and marketing expenses for our product (or
at least reasonable estimates).
Market research could be conducted to examine the current market landscape and the pricing strategies
adopted by competitors for similar products. Such research encompasses various approaches, each with
its own set of assumptions and uncertainties. By analysing this market research, we could estimate what
consumers might be willing to pay for a similar product and develop a pricing structure accordingly.
However, there are additional uncertainties that need to be considered. For instance:
Will there still be demand for our product when it is launched?
Will consumers have the financial means to purchase it at that time? (If there was a recession,
consumers may reduce their discretionary spending.)
Even if we price our product lower than our competitor(s), will consumers remain loyal to their
familiar brand and refrain from purchasing our product?
To address these uncertainties, we could conduct surveys to collect data on brand loyalty, make
predictions regarding consumers’ future willingness to pay, and assume that demand for our product will
be strong at launch. By gathering relevant data related to these uncertainties and incorporating logical
assumptions, we can create data-driven models to predict the outcomes of our proposed pricing
structures.
5
, Business Analytics:
Applied Modelling and Prediction
Solutions to end-of-chapter exercises
Chapter 2:
Descriptive statistics
