1. Multiple choices. Please choose one or more choices for each question.

(1) Below are two statements about clustering analysis.

Statement 1: The optimal number of segments should be that has the lowest SSE on the elbow chart.

Statement 2: Any two data points within the same cluster always have a shorter distance than two data points from different clusters do.

Which of these two statements are true? ( )

A. Only Statement 1 is true.

B. Only Statement 2 is true.

C. Both Statement 1 and 2 are true.

D. Neither Statement 1 nor 2 is true.

(2) Which statement(s) is right about Bass model of product diffusion?

A. The number of new adopters from the innovation channel is the highest at the beginning of the diffusion process

B. The number of new adopters from the imitation channel is the highest at the beginning of the diffusion process

C. The number of new adopters from the innovation channel is the highest at the peak new adoption time of the diffusion process

D. The number of new adopters from the imitation channel is the highest at the peak new adoption time of the diffusion process

2. Use the dataset “SUVDiffusion.csv,” which records the quarterly SUV sales data for 42 quarters, to answer the following questions.

(link: https://raw.githubusercontent.com/zoutianxin1992/MarketingAnalyticsPython/main/Marketing Analytics in Python/2022/final/SUVDiffusion.csv)

Suppose consumers do not repeat purchase an SUV after their first adoption.

(1) Estimate the Bass Model for SUV adoption. Report the estimated values of p, q, and M. Explain the meanings of these three coefficients.

(2) Report the number of people who newly adopt SUV in period t=50. Also report the total number of people who have adopted SUV until the end of period t=50.

(3) Report the forecasted adoptions of period 43-200 in the form of a plot, where the predicted adoptions are on the y-axis and the time (in quarters, from quarter 43 to quarter 200) is on the x-axis.

On average, Americans replace their SUVs around every 10 years. So, instead assuming consumers never repurchase SUV, suppose in each quarter on average 2.5% of the already adopters will repurchase a new SUV.

(4) After considering consumer repurchases, answer question (1)-(3) again.

(5) How are your answers changed after the consideration of consumer repurchases? Provide your explanation about why the changes happen.

3. You are the owner of a brand of energy drink, called ACTIVE. Excel sheet “active.csv” contains

the historical weekly sales data of your product. Ignore competitors in the market. (link:

https://raw.githubusercontent.com/zoutianxin1992/MarketingAnalyticsPython/main/Marketing Analytics in Python/2022/final/active.csv)

(1) Estimate the Scan*Pro model below:

ln �_� = � + �₁ ⋅ ln �_� + �₂ ⋅ �_� + �₃ ⋅ �_�,

where �_� and �_� are the unit sales and the price for ACTIVE in week t, respectively. �_� and �_� are the dummy variables for display and feature advertising in week t. Report the estimation results for �, �₁, �₂, and �₃ and interpret their meanings.

(2) Your marginal cost is $1.2, and you in-store display the product but do not feature advertise it. Based the result of question (1), what the optimal price must you charge for ACTIVE? What will be the resulting profit for ACTIVE?

(3) You can feature advertise ACTIVE in the market, which will cost you $100 per week. Based on the SCAN*PRO model, should you feature advertise ACTIVE? Suppose you still charge the optimal price and in-store display ACTIVE.

4. You work for electricity company ERU, which wants to customize text messages to its customers to effectively encourage their electricity savings. In a pilot study, ERU designed three different text messages (msg 1-3) and sent them to 500 customers. ERU then recorded each message’s efficacy in facilitating these consumers’ electricity saving behaviors.

Dataset “ElectricityUsage1.csv” records each customer’s average electricity usage at different periods of a day (morning 6am-12pm, afternoon 12pm-6pm, evening 6pm-12am, night 12am- 6am) before the pilot study. It also records the efficacies of the three messages to each customer. Below is a description of the variables.

(link: https://raw.githubusercontent.com/zoutianxin1992/MarketingAnalyticsPython/main/Marketing Analytics in Python/2022/final/ElectricityUsage1.csv)

MorningPctg: the customer’s electricity usage in the morning (6am-12pm) as a percentage of her total electricity usage before the pilot study

AfternoonPctg: the customer’s electricity usage in the afternoon (12pm-6pm) as a percentage of her total electricity usage before the pilot study

EveningPctg: the customer’s electricity usage in the evening (6pm-12am) as a percentage of her total electricity usage before the pilot study

NightPctg: the customer’s electricity usage at night (12pm-6am) as a percentage of her total electricity usage before the pilot study

Eff_Msg1: The efficacy of message 1 to the customer. 1 – lowest, 10 – highest Eff_Msg2: The efficacy of message 2 to the customer. 1 – lowest, 10 – highest Eff_Msg3: The efficacy of message 3 to the customer. 1 – lowest, 10 – highest

Some consumers may share similar underlying electricity usage patterns (for example, they use electricity mostly in the evening), and a text message’s efficacy may be similar for consumers who share a similar electricity usage pattern. To uncover these underlying patterns, you want to separate the 500 customers into different segments based on their electricity usage data (i.e., their MorningPctg, AfternoonPctg, EveningPctg, NightPctg). Consumers who belong to the same segment should have similar usage patterns, and those who belong to different segments should have different usage patterns.