Conjoint Analysis Project

We’ll explore a fascinating dataset from Lobster Land, a theme park, covering their operations from Memorial Day to Labor Day 2023. It was my project assignment with the Business Analyst master’s degree program at Boston University Metropolitan College.

With the 2024 summer season fast approaching, Lobster Land is exploring the possibility of adding a wooden roller coaster to its park. Wooden roller coasters, affectionately called “woodies,” have seen a resurgence in popularity among roller coaster enthusiasts.

To make an informed decision, Lobster Land conducted a survey to understand customer preferences for various roller coaster features. Using conjoint analysis and a linear regression model, the park analyzed the factors that influence customer ratings. Let’s dive into the findings and what they mean for the park’s decision-making process.

What I will touch:

• Jupiter Notebook and Data
• Understanding the Dataset
• Data Cleaning and Preparation
• Convert to Dummy Variable
• TIP — Data Type: Bool vs Numeric
• Building the Linear Regression Model
• Model Performance and Results
• Insights from the Coefficients
• Key Metrics
• Interpretation and Recommendations
• Limitations and Next Steps

Jupiter Notebook and Data

You can download and review my notebook…

You can review my Jupiter Notebook…

Step 1: Understanding the Dataset

Lobster Land Wooden Roller Coaster Survey

A. Data Shape

• There are 288 records and 8 variables.

B. Data Types

• There are actually 3 categorical variables, which are start_high, track_color, and bundleID.
• bundleID is a unique categorical variable in the dataset. There is no need to add that variable for our analysis.

Step 2: Data Cleaning and Preparation

A. Removing Unnecessary Columns

• Now, we have 7 columns.

B. Missing Values

• Suprisingly, we do not have missing values.

C. Convert to Dummy Variable

Categorical variable or looks numerical but represent categorical variables like our example (survey data range 1 to 10) can be converted to Dummy Variable (known as one-hot encoding),which means it creates separate binary columns for each category in a variable.

Each column represents whether a particular observation belongs to that category (1 for yes, 0 for no).

drop_first = True. will save us from the multicollinearity problem that would make our model unreliable.

TIP — Data Type: Bool vs Numeric

While bool is technically compatible with many machine learning models (because True is treated as 1 and False as 0), some libraries, such as statsmodels, may require explicit numeric types (int or float) for regression.

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For our linear model, we need to explicitly turn them to numeric:

3. Building the Linear Regression Model

To analyze the data, a linear regression model was built using the average rating (avg_rating) as the dependent variable and the roller coaster features as independent variables. Linear regression is a powerful tool for understanding how different factors influence an outcome.

Why Linear Regression?

Linear regression quantifies the relationship between predictors (features) and the outcome (average rating). It provides coefficients that indicate:

• Direction of impact: Whether a feature increases or decreases the rating.
• Magnitude of impact: How much the feature influences the rating.

Additionally, the statistical significance of each feature helps determine whether its effect is meaningful.

4. Model Performance and Results

A. Insights from the Coefficients

Coefficient Results

Significant Features (p-value < 0.05):

1. Start High (start_high_Yes):

• Coefficient: +1.10
• Rides that start at a high altitude received significantly higher ratings, likely because they offer an immediate thrill without a slow climb.

2. Max Speed (maxspeed_60 and maxspeed_80):

• Coefficients: +1.63 (60 mph), +1.44 (80 mph)
• Higher speeds were strongly associated with higher ratings, with 60 mph having the strongest effect.

3. Drop Height (drop_200 and drop_300):

• Coefficients: +1.05 (200 ft), +1.20 (300 ft)
• Larger drops were highly preferred, with the 300 ft drop being the most impactful.

4. Track Color (track_color_red):

• Coefficient: +1.78
• Respondents showed a clear preference for red tracks, which had the largest positive impact among all features.

5. Steepest Angle (steepest_angle_75):

• Coefficient: -0.49
• Surprisingly, steeper drops negatively impacted ratings. This may indicate that respondents found a 75° drop too intimidating.

6. Seats per Car (seats_car_4):

• Coefficient: -0.43
• Cars with 4 seats were less preferred than those with 2 seats, possibly due to perceived comfort or thrill differences.

Non-Significant Features (p-value > 0.05):

• Track Colors Green and White: These colors had negligible effects on ratings, suggesting that track color preferences are limited to specific options (e.g., red).

B. Key Metrics:

The regression model performed moderately well, explaining 46% of the variance in average ratings (R-squared = 0.46). While this indicates that the model captures key drivers of customer preferences, it also suggests that other factors (e.g., ride duration, theme) may influence ratings.

• Adjusted R-squared: 0.44 (accounts for the number of predictors to avoid overfitting).
• F-statistic (p-value < 0.0001): The model is statistically significant, meaning at least one feature significantly influences ratings.

C. Interpretation and Recommendations

Based on the findings, here’s how Lobster Land can design a roller coaster that appeals to its audience:

Must-Have Features:

1. High Start: Starting at a high altitude is a clear winner for creating excitement.
2. High Speed: Speeds of 60 mph or 80 mph are essential for a thrilling experience.
3. Large Drops: A 300 ft drop is ideal, but a 200 ft drop is also well-received.
4. Red Track: Choosing a red track color will likely attract more positive attention.

Features to Avoid:

1. Overly Steep Drops: A 75° drop could deter some riders, so a more moderate 50° drop is recommended.
2. Four-Seat Cars: Stick to two-seat cars for a more intimate and exciting ride experience.

D. Limitations and Next Steps

The multiple R-squared value for this model is 0.472, meaning that 47.2% of the variation in the average rating is explained by the variables included in the model.

While this demonstrates that the model captures some key drivers of customer preferences, it also highlights a significant limitation: 52.8% of the variation in the average rating remains unexplained. This suggests that there are other important factors influencing customer preferences that were not captured in the dataset, such as ride duration, theming, or even external factors like marketing efforts or ticket price.

Since more than half of the variation is unaccounted for, the model’s reliability is limited, and its results should be interpreted with caution. To improve the model’s accuracy and build greater trust in its predictions, additional variables should be collected and analyzed in future studies.

Your Thoughts?…

“I would like to hear”

• If you were part of the decision-making team, how would you address the unexplained 52.8% variation in customer ratings?
• Given that the model only explains 47.2% of the variation in ratings, what additional data might help improve the accuracy of the analysis?
• What other variables do you think should have been included in the survey to better understand customer preferences?
• Do you think Lobster Land should prioritize thrill factors like high speeds and large drops, or focus on family-friendly designs? Why?

…More…

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Sinem Atak