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\section{Data}
\label{sec:data}
% ==========================================================================

\subsection{Data Source}

The primary data for this study are drawn from Inside Airbnb
(\url{http://insideairbnb.com}), an independent, open-source project that
periodically scrapes publicly available listing information from the Airbnb
platform. The extracts provide a snapshot of every active listing, including
the nightly price, property and room type, geographic coordinates, host
profile variables, review scores, amenity counts, and free-text listing
names and descriptions.

Our sample covers the province of Quebec, Canada, encompassing the major
urban markets of Montr\'{e}al, Quebec City, Gatineau, Sherbrooke, and
Trois-Rivi\`{e}res, as well as popular tourism and resort regions including
the Laurentians (Mont-Tremblant, Saint-Sauveur), the Eastern Townships
(Magog, Bromont), the Charlevoix corridor, the
Saguenay--Lac-Saint-Jean region, and the Gasp\'{e}sie coast.

\subsection{Sample Construction}

Starting from the raw extract of 5,000 listings with 19 original variables,
we apply the following cleaning procedures:
%
\begin{enumerate}[leftmargin=2em]
    \item \textbf{Price validity.} Listings with a nightly price below
          \$10~CAD (17 observations) or above \$25,000~CAD (27 observations)
          are set to missing, eliminating data-entry errors and placeholder
          prices. After this step, 3,412 listings retain valid price
          observations.

    \item \textbf{Price transformations.} We construct the raw price, three
          Winsorized versions at the 1st/99th percentiles
          (\$38--\$10,822), 2nd/98th (\$46--\$8,117), and 5th/95th
          (\$63--\$4,921), plus natural log transformations.

    \item \textbf{Rating standardization.} Scores originally on a 0--100
          scale are converted to 0--5. Of the 5,000 listings, 810
          (16.2\%) lack a rating.

    \item \textbf{Geocoding validation.} Listings whose coordinates fall
          outside the geographic boundaries of Quebec
          (latitude $\in [44.5, 55.5]$, longitude $\in [-80.0, -56.0]$)
          are removed (6~observations).

    \item \textbf{Property type standardization.} Approximately 30 Inside
          Airbnb property type variants are mapped to six canonical
          categories: Rental unit, House, Cabin/Chalet, Condo, Apartment,
          and Other.
\end{enumerate}

After applying these filters, the analytical sample comprises
$N = 3{,}412$ listings with valid prices. Models incorporating additional
covariates with their own missing values use smaller effective samples
(reported alongside each specification).

\subsection{Variable Definitions}

We organize the variables into seven categories. The dependent variable
is the natural logarithm of the nightly listing price in Canadian dollars
($\ln p_i$). The log transformation addresses the strong right skew of the
raw price distribution (mean = \$1,115; median = \$219; standard deviation
= \$2,253) and yields coefficients interpretable as approximate percentage
changes via $\text{Premium}(\%) = 100 \times (\exp(\hat{\beta}) - 1)$.

\textit{Structural characteristics} ($\mathbf{S}_i$) capture the physical
attributes: bedrooms (mean~=~2.08), bathrooms (mean~=~1.28), guest capacity
(mean~=~5.31), log-transformed counterparts, per-guest ratios, property type
dummies (entire home = 48.1\%, private room = 35.5\%), a large-capacity
indicator ($\geq 8$ guests), quadratic and interaction terms.

\textit{Amenity indices} ($\mathbf{A}_i$) are constructed from the raw
amenity count (mean~=~44.9, range 3--109): luxury index, business travel
index, family comfort index, leisure index, remote work index, and
amenity richness index, all normalized to $[0, 1]$.

\textit{Host attributes} ($\mathbf{H}_i$) include Superhost status
(52.3\%), Guest Favorite badge (33.4\%), multi-listing host indicator,
and a Superhost $\times$ entire-home interaction.

\textit{Reputation variables} ($\mathbf{R}_i$) comprise the overall review
score (mean~=~4.80 on a 0--5 scale), log review count, quality score,
reputation score, cleanliness premium indicator, and missing-rating flag.

\textit{Locational variables} ($\mathbf{L}_i$) include Haversine distance
to the nearest city centre (22 municipalities), local listing density
within 500m (mean~=~14.7, max~=~125) and 1~km, local average price
within 500m and 1~km, and a $K$-means spatial cluster ($K = 20$).

\textit{Text-derived features} ($\mathbf{N}_i$) include title length,
seven bilingual keyword scores, and 10 TF-IDF/SVD embedding components
capturing 16.98\% of lexical variance.

\subsection{Descriptive Statistics}

Table~\ref{tab:summary} reports descriptive statistics for the key
variables. The price distribution is strongly right-skewed: the mean
(\$1,115) exceeds the median (\$219) by a factor of five, confirming the
appropriateness of the log transformation.

\begin{table}[!htbp]
\centering
\caption{Summary Statistics of Key Variables}
\label{tab:summary}
\begin{threeparttable}
\begin{tabular}{lrrrrrrr}
\toprule
Variable & Mean & Std.\ Dev. & Min & P25 & Median & P75 & $N$ \\
\midrule
Price (\$CAD) & 1,115 & 2,253 & 10.5 & 125.0 & 219.2 & 1,139 & 3,412 \\
Log price & 5.87 & 1.42 & 2.36 & 4.83 & 5.39 & 7.04 & 3,412 \\
Bedrooms & 2.08 & 1.53 & 0 & 1 & 2 & 3 & 5,000 \\
Bathrooms & 1.28 & 1.05 & 0 & 1 & 1 & 2 & 5,000 \\
Guest capacity & 5.31 & 3.37 & 1 & 2 & 4 & 7 & 5,000 \\
Amenities count & 44.9 & 16.0 & 3 & 34 & 45 & 56 & 5,000 \\
Rating (0--5) & 4.80 & 0.23 & 2.25 & 4.73 & 4.86 & 4.96 & 4,190 \\
Num.\ reviews & 62.7 & 85.0 & 0 & 10 & 33 & 82 & 4,275 \\
Quality score & 93.8 & 41.9 & 0 & 94.5 & 107.9 & 121.0 & 5,000 \\
Num.\ images & 27.9 & 19.2 & 0 & 14 & 23 & 36 & 5,000 \\
Is Superhost & 0.52 & 0.50 & 0 & 0 & 1 & 1 & 5,000 \\
Is Guest Favorite & 0.33 & 0.47 & 0 & 0 & 0 & 1 & 5,000 \\
Pets allowed & 0.29 & 0.46 & 0 & 0 & 0 & 1 & 5,000 \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\footnotesize
\item \textit{Notes:} This table reports descriptive statistics for the
main variables used in the empirical analysis. Price is measured in
Canadian dollars per night. Rating is on a 0--5 scale. Binary variables
are coded as 0/1.
\end{tablenotes}
\end{threeparttable}
\end{table}

Table~\ref{tab:price_type} presents the price distribution by property type.
Condos and apartments exhibit the highest mean prices, driven by urban
premium listings, while Cabin/Chalet listings show moderate means with
substantial variation reflecting Quebec's diverse cottage and ski resort
market.

\begin{table}[!htbp]
\centering
\caption{Price Distribution by Property Type (\$CAD)}
\label{tab:price_type}
\begin{threeparttable}
\begin{tabular}{lrrrrrr}
\toprule
Property Type & Mean & Median & Std.\ Dev. & Min & Max & $N$ \\
\midrule
Apartment & 1,276 & 201 & 3,328 & 15 & 18,117 & 77 \\
Cabin/Chalet & 969 & 237 & 2,215 & 48 & 23,321 & 691 \\
Condo & 1,344 & 210 & 2,343 & 49 & 14,577 & 237 \\
House & 1,058 & 223 & 2,206 & 18 & 22,811 & 679 \\
Other & 1,203 & 170 & 2,727 & 11 & 23,625 & 554 \\
Rental unit & 1,136 & 247 & 1,925 & 14 & 24,928 & 1,174 \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\footnotesize
\item \textit{Notes:} This table reports the distribution of nightly
prices (CAD) by property type for listings with valid prices ($N = 3{,}412$).
\end{tablenotes}
\end{threeparttable}
\end{table}

\subsection{Correlation Structure}

Table~\ref{tab:correlations} presents pairwise Pearson correlations among
the key continuous variables. Bedrooms, bathrooms, and guest capacity are
moderately to strongly intercorrelated ($r = 0.64$--$0.81$), motivating
the inclusion of per-guest ratios and log transformations to mitigate
multicollinearity. The number of reviews shows a negative correlation
with log price ($r = -0.24$), suggesting that more frequently booked
listings tend to be lower-priced.

\begin{table}[!htbp]
\centering
\caption{Correlation Matrix of Key Variables}
\label{tab:correlations}
\begin{threeparttable}
\small
\begin{tabular}{lccccccc}
\toprule
 & log\_price & bed & bath & guests & amen. & rating & reviews \\
\midrule
log\_price & 1.000 & & & & & & \\
Bedrooms & 0.111*** & 1.000 & & & & & \\
Bathrooms & 0.138*** & 0.704*** & 1.000 & & & & \\
Guests & 0.072*** & 0.806*** & 0.637*** & 1.000 & & & \\
Amenities & $-$0.051** & 0.322*** & 0.290*** & 0.370*** & 1.000 & & \\
Rating & 0.006 & 0.129*** & 0.157*** & 0.113*** & 0.274*** & 1.000 & \\
Reviews & $-$0.236*** & $-$0.061** & $-$0.049** & $-$0.029 & 0.095*** & 0.072*** & 1.000 \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\footnotesize
\item \textit{Notes:} Pearson correlation coefficients.
***, **, and * indicate statistical significance at the 1\%, 5\%, and
10\% levels, respectively.
\end{tablenotes}
\end{threeparttable}
\end{table}

\subsection{Price Distribution}

Figure~\ref{fig:price_dist} displays the distribution of nightly prices.
The raw price distribution is strongly right-skewed, with the median
(\$219) substantially below the mean (\$1,115).
Figure~\ref{fig:logprice_dist} shows the log-transformed distribution,
which is approximately symmetric.

\begin{figure}[!htbp]
\centering
\includegraphics[width=0.85\textwidth]{01_price_distribution.png}
\caption{Distribution of Nightly Listing Prices (\$CAD)}
\label{fig:price_dist}
\begin{minipage}{0.9\textwidth}
\footnotesize
\textit{Notes:} This figure plots the histogram and kernel density estimate
of nightly listing prices in Canadian dollars. The vertical dashed lines
indicate the mean and median.
\end{minipage}
\end{figure}

\begin{figure}[!htbp]
\centering
\includegraphics[width=0.85\textwidth]{02_log_price_distribution.png}
\caption{Distribution of Log Nightly Prices}
\label{fig:logprice_dist}
\begin{minipage}{0.9\textwidth}
\footnotesize
\textit{Notes:} This figure plots the histogram and kernel density estimate
of $\ln(\text{price})$. The approximately symmetric distribution confirms
the suitability of the log-linear specification.
\end{minipage}
\end{figure}

\subsection{Geographic Coverage}

Figure~\ref{fig:map} maps the spatial distribution of listings across
Quebec, with colour indicating nightly price. The majority of listings
are concentrated in Montr\'{e}al, with secondary clusters in Quebec City,
the Laurentian resort corridor, and the Eastern Townships. Local listing
density reaches 125 within 500 metres in central Montr\'{e}al.

\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{03_price_map.png}
\caption{Geographic Distribution of Airbnb Listings in Quebec}
\label{fig:map}
\begin{minipage}{0.9\textwidth}
\footnotesize
\textit{Notes:} Each point represents one listing, coloured by nightly
price (capped at the 99th percentile for visual clarity). Coordinates are
latitude/longitude (WGS-84).
\end{minipage}
\end{figure}

\subsection{Price Variation by Property Type and Neighbourhood}

Figure~\ref{fig:price_neighbourhood} displays boxplots of nightly prices
for the top 20 cities by listing count, and Figure~\ref{fig:price_room}
shows the price distribution by property type.

\begin{figure}[!htbp]
\centering
\includegraphics[width=0.95\textwidth]{04_price_by_neighbourhood.png}
\caption{Nightly Price Distribution by City (Top 20)}
\label{fig:price_neighbourhood}
\begin{minipage}{0.9\textwidth}
\footnotesize
\textit{Notes:} Boxplots of nightly prices for the 20 cities with the
most listings, ordered by median price.
\end{minipage}
\end{figure}

\begin{figure}[!htbp]
\centering
\includegraphics[width=0.85\textwidth]{05_price_by_room_type.png}
\caption{Price Distribution by Property Type}
\label{fig:price_room}
\begin{minipage}{0.9\textwidth}
\footnotesize
\textit{Notes:} Violin plots of nightly prices by property type. Inner
markers indicate quartiles.
\end{minipage}
\end{figure}