Communicating a Data Modeling Analysis

Biagio Palese

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Artwork by @allison_horst

Class Objective

  • Review the steps used to complete a complete data analysis.
  • Communicate the results of the complete data analysis.

Hotel Analysis Scenario

OptimaHotel Insights has been tasked by multiple hotel chains to develop a predictive model that can accurately forecast Average Daily Rates (ADR) based on various hotel features.

ADR Analysis Deliverables

  • A comprehensive report/presentation detailing the entire data analysis.
  • A fully functional predictive pricing model with satisfactory prediction accuracy.
  • Offer strategic recommendations based on the model insights, feature importance, and predicted impacts on ADR.

Step 1: Exploring the Dataset

The hotel_data dataset used in this case study contains comprehensive information on various attributes and performance metrics of 3000 hotels across major U.S. cities.

It is meticulously curated1 to support predictive analyses focused on predicting and optimizing the average daily rate (ADR) for these properties.

This dataset includes realistic and detailed data, encompassing a wide range of features crucial for developing predictive pricing models.

Dataset Dimensions
rows_number columns_number
3000 22

Dataset Glimpse
Column Name Data Type Example Values
id numeric 1, 2, 3
num_rooms numeric 33, 71, 150
location_quality character Excellent, Excellent, Good
star_rating numeric 1, 5, 3
review_score numeric 1.84, 1.88, 2.93
occupancy_rate numeric 71.65, 52.29, 97.43
amenities_score numeric 3, 5, 1
business_facilities numeric 0, 1, 1
leisure_facilities numeric 1, 1, 1
distance_to_city_center numeric 7.92, 4.85, 8.58
average_daily_rate numeric 98.22, 98.73, 106.56
city character Chicago, New York, Los Angeles
hotel_chain character Hilton, Hyatt, Marriott
month numeric 1, 5, 12
season character Winter, Spring, Winter
number_of_bookings numeric 53, 61, 58
revPAR numeric 70.37, 51.62, 103.82
average_length_of_stay numeric 4.45, 3.09, 3.6
competitors_average_price numeric 88.56, 84.46, 131.51
transport_accessibility_score numeric 3.67, 6.3, 6.3
customer_satisfaction_index numeric 81.57, 94.62, 91.12
cancellation_rate numeric 0.01, 0.1, 0.14

ADR Descriptive Stats
min_average_daily_rate avg_average_daily_rate median_average_daily_rate max_average_daily_rate sd_average_daily_rate
49.87 95.87045 95.825 141.83 14.98696

ADR Descriptive Stats by City
city min_average_daily_rate avg_average_daily_rate median_average_daily_rate max_average_daily_rate sd_average_daily_rate
Chicago 53.45 96.02526 96.045 141.83 15.48101
Los Angeles 49.87 95.56752 95.160 135.78 14.67615
Miami 54.23 96.19310 96.105 139.10 14.19395
New York 57.49 95.71646 95.930 140.88 15.10470
San Francisco 51.98 95.88067 96.085 140.77 15.45662

ADR Descriptive Stats by Hotel Chain
hotel_chain min_average_daily_rate avg_average_daily_rate median_average_daily_rate max_average_daily_rate sd_average_daily_rate
Hilton 55.12 95.92 96.00 140.77 15.51
Hyatt 54.78 95.28 95.08 141.83 15.24
InterContinental 51.94 96.31 96.67 139.10 14.70
Marriott 57.47 95.87 96.32 140.88 14.52
Sheraton 49.87 96.01 95.93 139.65 14.98

Step 2: Manipulating the Data

Based on the above exploration the following minor manipulations1 are required:

hotel_clean <- hotel_data |> 
   filter(average_daily_rate    >60 &average_daily_rate <130) |> #removes outliers and gives normal distribution
   filter(revPAR    >5 &revPAR  <118) |> 
   mutate(miles_distance_to_city_center= distance_to_city_center/1.6) |> 
   select(-distance_to_city_center)

Step 3: Checking Correlations

Given that we are working on a new dataset and that we are not super familiar with hotel data, it is worth to take a look at the correlation of our numerical variables.

Correlation Matrix

Correlation Matrix Arranged By ADR
variables average_daily_rate num_rooms star_rating review_score occupancy_rate amenities_score business_facilities leisure_facilities month number_of_bookings revPAR average_length_of_stay competitors_average_price transport_accessibility_score customer_satisfaction_index cancellation_rate miles_distance_to_city_center
average_daily_rate 1.0000 0.0043 0.1443 0.0301 0.2323 0.0145 0.2832 0.4994 -0.0110 0.0274 0.5704 -0.0028 0.5749 -0.0041 -0.0271 0.0105 0.0031
competitors_average_price 0.5749 -0.0096 0.0878 0.0044 0.1385 0.0080 0.1251 0.2872 0.0103 0.0047 0.3305 0.0074 1.0000 -0.0087 -0.0033 0.0163 -0.0121
revPAR 0.5704 0.0071 0.0790 0.0221 0.9228 0.0000 0.1011 0.1582 -0.0039 -0.0080 1.0000 -0.0181 0.3305 -0.0175 -0.0023 0.0076 0.0003
leisure_facilities 0.4994 -0.0099 0.0177 0.0034 -0.0350 0.0122 -0.0179 1.0000 -0.0263 0.0336 0.1582 0.0042 0.2872 -0.0027 -0.0247 0.0020 -0.0020
business_facilities 0.2832 -0.0061 0.0068 -0.0195 -0.0080 -0.0383 1.0000 -0.0179 -0.0064 -0.0125 0.1011 -0.0120 0.1251 -0.0008 0.0062 -0.0243 0.0100
occupancy_rate 0.2323 0.0065 0.0254 0.0148 1.0000 -0.0052 -0.0080 -0.0350 0.0014 -0.0226 0.9228 -0.0202 0.1385 -0.0220 0.0076 0.0013 -0.0005
star_rating 0.1443 0.0044 1.0000 -0.0049 0.0254 -0.0035 0.0068 0.0177 0.0258 0.0138 0.0790 -0.0243 0.0878 0.0094 -0.0128 0.0085 0.0235
review_score 0.0301 0.0123 -0.0049 1.0000 0.0148 0.0063 -0.0195 0.0034 0.0223 0.0129 0.0221 -0.0317 0.0044 -0.0135 0.0010 -0.0464 0.0005
number_of_bookings 0.0274 -0.0037 0.0138 0.0129 -0.0226 0.0175 -0.0125 0.0336 -0.0371 1.0000 -0.0080 0.0183 0.0047 -0.0121 0.0009 -0.0113 0.0100
amenities_score 0.0145 -0.0318 -0.0035 0.0063 -0.0052 1.0000 -0.0383 0.0122 0.0054 0.0175 0.0000 -0.0304 0.0080 -0.0131 0.0304 -0.0188 0.0069
cancellation_rate 0.0105 -0.0024 0.0085 -0.0464 0.0013 -0.0188 -0.0243 0.0020 -0.0157 -0.0113 0.0076 0.0056 0.0163 -0.0037 0.0051 1.0000 0.0042
num_rooms 0.0043 1.0000 0.0044 0.0123 0.0065 -0.0318 -0.0061 -0.0099 0.0145 -0.0037 0.0071 -0.0222 -0.0096 0.0135 0.0309 -0.0024 0.0068
miles_distance_to_city_center 0.0031 0.0068 0.0235 0.0005 -0.0005 0.0069 0.0100 -0.0020 -0.0129 0.0100 0.0003 -0.0263 -0.0121 0.0089 -0.0117 0.0042 1.0000
average_length_of_stay -0.0028 -0.0222 -0.0243 -0.0317 -0.0202 -0.0304 -0.0120 0.0042 -0.0223 0.0183 -0.0181 1.0000 0.0074 0.0238 -0.0063 0.0056 -0.0263
transport_accessibility_score -0.0041 0.0135 0.0094 -0.0135 -0.0220 -0.0131 -0.0008 -0.0027 -0.0254 -0.0121 -0.0175 0.0238 -0.0087 1.0000 -0.0210 -0.0037 0.0089
month -0.0110 0.0145 0.0258 0.0223 0.0014 0.0054 -0.0064 -0.0263 1.0000 -0.0371 -0.0039 -0.0223 0.0103 -0.0254 0.0193 -0.0157 -0.0129
customer_satisfaction_index -0.0271 0.0309 -0.0128 0.0010 0.0076 0.0304 0.0062 -0.0247 0.0193 0.0009 -0.0023 -0.0063 -0.0033 -0.0210 1.0000 0.0051 -0.0117

Step 4: Data Splitting

When it comes to supervised data modeling one of the most adopted method to evaluate multiple models is to split the data into a training set and a test set from the beginning.

# Split the data
set.seed(123)# setting a seed will ensure reproducibility
hotel_split <- initial_split(hotel_clean, prop = 0.75) # define the split and its data proportion
hotel_train <- training(hotel_split) #create a train set
hotel_test <- testing(hotel_split)#create a test set

Hotel train

Training Dataset Dimensions
rows_number columns_number
2192 22

Hotel test

Test Dataset Dimensions
rows_number columns_number
731 22

Step 5: Setting up the Recipes

Creating recipes is a critical step because it allows to define the model formula and specify any preprocessing steps to the original dataset.

Recipe 1

recipe1 <- recipe(average_daily_rate ~ revPAR + competitors_average_price, data = hotel_train)

Recipe 2

recipe2 <- recipe(average_daily_rate ~ revPAR + competitors_average_price+ location_quality+ star_rating + season, data = hotel_train)|> 
  step_dummy(all_nominal_predictors())

Recipe 3

recipe3 <- recipe(average_daily_rate ~ ., data = hotel_train)|> 
  step_dummy(all_nominal_predictors())

Step 6: Specifying the Models

We specify two models using parsnip:

  1. a lm engine linear regression;

  2. a glmnet engine lasso regression1.

Model 1

# Linear regression with lm
linear_mod_reg <- linear_reg() |>
  set_engine("lm") |>
  set_mode("regression")

Model 2

# Lasso regularized linear regression with glmnet
linear_mod_lasso <- linear_reg(penalty = 0.1, mixture = 1) |>
  set_engine("glmnet") |>
  set_mode("regression")

Step 7: Fitting Models using Workflows

Next, we fit the models to the hotel_train dataset, so that we can compare their predictions performance on hotel_test.

This is accomplished by embedding the model specifications within workflows that also incorporate our preprocessing recipes.

Lasso recipe 3 model workflow

recipe3_workflow_lasso <- workflow() |>
  add_recipe(recipe3) |>
  add_model(linear_mod_lasso) |>
  fit(data = hotel_train)#we create and fit the workflow on just the train set

Lasso recipe 3 model workflow output

══ Workflow [trained] ══════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: linear_reg()

── Preprocessor ────────────────────────────────────────────────────────────────
1 Recipe Step

• step_dummy()

── Model ───────────────────────────────────────────────────────────────────────

Call:  glmnet::glmnet(x = maybe_matrix(x), y = y, family = "gaussian",      alpha = ~1) 

   Df  %Dev Lambda
1   0  0.00 8.0810
2   2  8.03 7.3630
3   2 15.16 6.7090
4   3 21.82 6.1130
5   3 28.36 5.5700
6   3 33.80 5.0750
7   3 38.31 4.6240
8   3 42.06 4.2130
9   3 45.17 3.8390
10  3 47.75 3.4980
11  3 49.89 3.1870
12  4 52.07 2.9040
13  4 54.14 2.6460
14  4 55.86 2.4110
15  4 57.28 2.1970
16  5 58.72 2.0020
17  5 60.01 1.8240
18  5 61.09 1.6620
19  6 62.14 1.5140
20  6 63.02 1.3800
21  7 65.04 1.2570
22  7 69.61 1.1450
23  7 73.40 1.0440
24  7 76.56 0.9510
25  8 79.21 0.8665
26  9 81.38 0.7895
27  9 83.19 0.7194
28  9 84.70 0.6555
29  9 85.96 0.5972
30  9 87.00 0.5442
31  9 87.86 0.4958
32  9 88.58 0.4518
33  9 89.18 0.4117
34  9 89.67 0.3751
35  9 90.09 0.3418
36  9 90.43 0.3114
37  9 90.71 0.2837
38  9 90.95 0.2585
39 10 91.15 0.2356
40 10 91.31 0.2146
41 10 91.45 0.1956
42 10 91.57 0.1782
43 10 91.66 0.1624
44 11 91.74 0.1479
45 12 91.81 0.1348
46 14 91.87 0.1228

...
and 26 more lines.

Step 8: Making Predictions

Then we use the models built on the training set to make predictions on our test set.

By doing so we will have both the actual values and the predicted values and we can assess the model performance.

Lasso recipe 3 model actual ADR values vs predicted

ADR actual vs predicted values
adr pred_adr
104.940000 104.782852
97.320000 96.591127
68.120000 79.503404
108.070000 111.700405
114.530000 104.066156
118.040000 110.767541
109.080000 106.135489
104.270000 106.979850
66.850000 76.432982
73.480000 80.028296

Step 9: Assess Models Performance

While seeing the predictions next to the actual values can already provide some insights on the goodness of the model.

In regression analysis, model performance is evaluated using specific metrics that quantify the model’s accuracy and ability to generalize.

Three fundamental metrics are Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and R-squared (R²).

Full Metrics Table
.metric .estimate model
mae 2.9318 reg_model_recipe3
mae 2.9770 lasso_model_recipe3
mae 7.9723 lasso_model_recipe2
mae 7.9748 reg_model_recipe2
mae 8.2290 reg_model_recipe1
mae 8.2325 lasso_model_recipe1
rmse 4.0948 reg_model_recipe3
rmse 4.1122 lasso_model_recipe3
rmse 9.7966 reg_model_recipe2
rmse 9.8012 lasso_model_recipe2
rmse 10.1661 reg_model_recipe1
rmse 10.1682 lasso_model_recipe1
rsq 0.4687 reg_model_recipe1
rsq 0.4687 lasso_model_recipe1
rsq 0.5067 reg_model_recipe2
rsq 0.5068 lasso_model_recipe2
rsq 0.9138 reg_model_recipe3
rsq 0.9145 lasso_model_recipe3

By looking at the metrics table recipe 3 lasso is the best model. We excluded the recipe 3 regression model because of a warning highlighting issues during its fit.

Full Metrics Table with Best Model
.metric .estimate model
mae 2.9318 reg_model_recipe3
mae 2.9770 lasso_model_recipe3
rmse 4.0948 reg_model_recipe3
rmse 4.1122 lasso_model_recipe3
rsq 0.9138 reg_model_recipe3
rsq 0.9145 lasso_model_recipe3

Step 10: Visualizing Prediction Results

Visualizing the prediction results can provide additional insights into model performance.

You should plot the predicted vs actual values and the residuals to visually assess how well the model is capturing the underlying relationship in the data.

The charts above clearly show how overall the best model does a pretty good job in predicting our dependent variable.

However, there is room for improvement because in both charts we noticed some deviation from the desired line.

Visual interpretations provide valuable insights into model performance but should be complemented with quantitative metrics (like RMSE, MAE and R²) for a comprehensive evaluation.

The plots help identifying patterns or biases not immediately apparent from numerical metrics alone.

Step 11: Model Interpretation

Given that recipe3 lasso regression model gives the best prediction results both in terms of metrics and visualizations.

We can then conclude that this model is the best/most optimal model among those tested. Thus, we will proceed to interpret its results.

Zero Coefficients Variables do not have a statistically significant linear relationship with ADR after accounting for other variables and the regularization penalty.

Removed Predictors
term estimate penalty
num_rooms 0.000000 0.100000
month 0.000000 0.100000
number_of_bookings 0.000000 0.100000
average_length_of_stay 0.000000 0.100000
transport_accessibility_score 0.000000 0.100000
miles_distance_to_city_center 0.000000 0.100000
city_Los.Angeles 0.000000 0.100000
city_Miami 0.000000 0.100000
city_New.York 0.000000 0.100000
city_San.Francisco 0.000000 0.100000
hotel_chain_Hyatt 0.000000 0.100000
hotel_chain_Marriott 0.000000 0.100000
hotel_chain_Sheraton 0.000000 0.100000
season_Spring 0.000000 0.100000
season_Summer 0.000000 0.100000
season_Winter 0.000000 0.100000

Non-Zero Coefficients Variables are influencing factors for ADR and should be considered in pricing strategies.

Included Predictors
term estimate penalty
(Intercept) 83.405263 0.100000
star_rating 0.171419 0.100000
review_score 0.106057 0.100000
occupancy_rate −1.143306 0.100000
amenities_score 0.015416 0.100000
business_facilities 1.707039 0.100000
leisure_facilities 2.757357 0.100000
revPAR 1.243648 0.100000
competitors_average_price 0.052455 0.100000
customer_satisfaction_index −0.004978 0.100000
cancellation_rate −0.569816 0.100000
location_quality_Excellent 1.888997 0.100000
location_quality_Good 0.951980 0.100000
location_quality_Poor −0.754707 0.100000
hotel_chain_InterContinental 0.000330 0.100000

Intercept: $83.4 represent the expected ADR when the categorical predictors are in their baseline category (the first value in alphabetical order) and the numerical predictors are zero or at their lowest practical/observed levels.

Intercept Only Table
term estimate
(Intercept) 83.405263

Star Rating: For one additional star, ADR increases by approximately $0.171, assuming all other variables remain constant.

This means that moving from 1-star to a 5-star hotel, which is an increase of 4 stars, would lead to an estimated increase of 0.171 x 4 = $0.684 in ADR1.

Star Rating Only Table
term estimate
star_rating 0.171419

Review Score: For one point increase in the review score (on a scale of 1 to 5), ADR increases by $0.106 given all other variables staying constant.

Review Score Only Table
term estimate
review_score 0.106057

This shows the value customers place on higher-rated hotels, which can command higher prices but the impact is surprisingly small.

Occupancy Rate: For one percentage point increase in occupancy rate, ADR decreases by $1.14. Surprisingly, higher occupancy rates do not correspond with higher ADR.

Occupancy Rate Only Table
term estimate
occupancy_rate −1.143306

It’s possible that in an effort to maintain high occupancy levels, hotels might be underpricing their rooms, thus not maximizing potential revenue.

Business Facilities & Leisure Facilities: Hotels with business and leisure facilities can charge an additional $1.71 and $2.76, respectively, on ADR.

Business Facilities & Leisure Facilities Only Table
term estimate
business_facilities 1.707039
leisure_facilities 2.757357

However, these amenities impact does not seem substantial at first glance, particularly when considering the potential costs associated with maintaining them.

RevPAR (Revenue per Available Room): This variable is an important hospitality metrics. RevPAR combines the effects of room rates and occupancy levels. For one dollar increase in RevPAR, ADR increases by $1.24.

RevPAR Only Table
term estimate
revPAR 1.243648

Competitors Average Price: For one dollar increase in competitors' average prices, ADR increases by only $0.0525.

Competitors Average Price Only Table
term estimate
competitors_average_price 0.052455

The strategy of not matching the price increases fully could reflect a positioning approach where hotels aim to offer slightly lower prices to attract price-sensitive customers or to increase market share by becoming a more economical option within their competitive set.

Customer Satisfaction Index: For every one-unit increase in the customer satisfaction index, ADR decreases by approximately $0.005, assuming other factors remain constant.

Customer Satisfaction Index Only Table
term estimate
customer_satisfaction_index −0.004978

The negative coefficient suggests a potential under utilization of customer satisfaction. Thus, increases in customer satisfaction do not translate into higher ADR.

Cancellation Rate: For each percentage point increase in cancellation rates, ADR decreases by $0.570.

Cancellation Rate Only Table
term estimate
cancellation_rate −0.569816

While this drop in price can mitigate the risk of empty rooms, it also suggests potential revenue losses or instability in booking patterns.

Location Quality: Being in an Excellent location increases the ADR by $1.89, while being in a Good location increases it by $0.952, compared to our baseline, Average location.

Location Quality Only Table
term estimate
location_quality_Excellent 1.888997
location_quality_Good 0.951980
location_quality_Poor −0.754707

Being in a Poor location decreases it by $0.755 compared to Average. Hotels are clearly underselling their premium locations.

Step 12: Making Real Predictions

Once you have assessed the model prediction performance and interpreted the results, the final step is to use the best/most optimal model to make predictions on a hotel dataset that does not contain ADR.

New dataset ADR predictions

New Hotel Data ADR Values Predictions
forecasted_adr
112.140946
241.006373
113.691424
68.688388
140.039062
137.975722
63.926277
86.710203
170.197796
63.491527

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Artwork by @allison_horst