Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 8, No. 3, 2023 

 

234 

Data	Analysis	and	Research	Based	on	Second‐hand	
Sailboats	
Xiaolin Liu1, * 

1School of Modern Posts, Chongqing University of Posts and Telecommunications, Chongqing, China 
*Corresponding author: 2248301625@qq.com 

 

Abstract: With the rise of sailing sports, the second-hand sailing trading market shows a great potential for development. We 
research a thorough research on the pricing of second-hand sailing. Firstly, the linear regression model and decision tree 
regression model use machine learning algorithm to accurately evaluate the sailing price; secondly, the two-factor analysis 
method is used to analyze the influence of manufacturer and geographical region on the market price; and finally, the accuracy 
of the model is evaluated by paired sample T-test and Pearson correlation analysis methods. 

Keywords: Linear regression, Decision tree, Two-factor analysis, Paired sample T-test, Pearson correlation analysis. 
 

1. Introduction 
Based on an in-depth survey of the sailing industry, it is 

found that although there were some fluctuations in the global 
sailing market when the COVID-19 epidemic first occurred 
in 2020, so far, the sailing industry has basically escaped the 
impact of the epidemic and maintained a steady increase in 
order volume for the third consecutive year. GOB recorded an 
impressive 1024 projects under construction or ordered, up 
24.7% from 821 last year. Therefore, the research on sailing 
pricing is beneficial to the relevant enterprises to make a 
forecast on the consumption scale and growth trend of sailing 
products, and thus help sailing manufacturers to grasp the 
demand status and demand trend of various user groups for 
sailing products. 

2. Model Building and Solution 

2.1. Data acquisition and preprocessing 
By finding the relevant data, found that the world bank, 

international freight and trade association, the world economy 
BBS website and SailboatData.com-the worlds largest 
sailboat database website there are a lot of sailing we need its 
performance related data, using web crawler technology, get 
web information, the content we have in the web need 
keyword extraction, get the final data and storage. Through 
data screening and processing of the data, we finally selected 
ship width, displacement, sail area, low water level, draft, 
cargo throughput in different regions, GDP, GDP per capita, 
and the average proportion of total logistics cost to GDP as 
other predictive factors that may affect the pricing to further 
analyze the pricing of sailing boats. 

2.2. Build and solve the multivariate linear 
regression model 

The solution of the multivariate linear regression model is 
basically similar to that of the unary linear regression model, 
but in this case, there are many independent variables 
affecting the listing price of sailing boats, so it is difficult to 
solve the problem by setting up parameters by itself. To 
further simplify the solution process, we process the data and 

solve the model with the help of the library and methods 
brought in Python. Then the linear regression algorithm in 
machine learning is introduced to process the training values 
and test values, and find the appropriate parameters, so that 
the linear weighted values of the respective variables are 
closer to the real listing price. 

Set the assumption function: 
 

Y ω X b          (1) 
 
Where 𝑌𝑖 represents the test data, 𝑋𝑖 represents the sample 

data, and b represents the bias measure used to adjust the data 
results. According to the law of large numbers and the central 
limit theorem, the error of the true value and the predicted 
value of the market price is ε ~N(0, δ2), and then the loss 
function is set: 

 

loss
∑ ωTXi b Y

2n
i 1

n
            (2) 

 
The loss function value is used as the mean variance to 

calculate the error of the total sample. Then you can 
continuously fit the results, strengthen the training set, and 
obtain the most suitable set of ω and b values, so that the 
verification set continues to approximate the real value. 

To further evaluate the fit of the regression model, we also 
define the MAPE function to calculate the mean absolute 
error of the training and validation sets. The formula for 
setting the average absolute error is as follows: 

 
MEA ∑ pred y            (3) 

 
After obtaining the final training and validation sets, the 

coefficient of determination, r-2., can be calculated to 
determine the fit of the regression equation. Set the formula 
for calculating the coefficient of determination: 

 

𝑟
∑

∑
           (4) 

 

 



 

235 

 

Figure 1. Prediction chart of monohull test data 

 

 

Figure 2. Prediction chart of catamaran test data 

 
From the prediction plots of the test data in Figure 1 and 

Figure 2, it can be seen that there is a large difference between 
the real values and the predicted values of monohulls and 
catamarans, and there is an error in the prediction value of this 
model, and the training model parameters still need to be 
adjusted. The accuracy of predictions can be improved by 
increasing the proportion of training or cross-validation. 

3. Model Optimization 
Taking a catamaran as an example, the use of linear 

regression to fit a catamaran is not completely realistic, and 
the error between the predicted value and the true value of the 
model is large. Therefore, the catamaran needs to invoke other 
models to optimize its results. Since there are many 
independent variables that affect the listing price of 
catamarans, it can be assumed that the variables that have less 
weight on the price of these independent variables infect the 
model and lead to inaccurate results. The above problem is in 
line with the decision tree model, and in the subtree of the 
factors influencing the catamaran listing price, we can use 
pruning treatment to remove the secondary influencing 
factors and prevent overfitting of the model. 

First of all, the data needs to be preprocessed, using the 
concept of information entropy to exclude redundant 
information. To set the information entropy formula: 

 
H x ∑ p x log p x        (5) 

 
When processing a large amount of data, in order to prevent 

important factors from being removed and shorten the 
training time, we also choose the pre-pruning method, and set 
the accuracy and recall for the pre-pruning to determine 
whether the target information is discarded. 

Accuracy formula: 
  

Precision TP FP TP           (6) 
  
Recall formula: 
 

Recall TP TN TP            (7) 
 
Finally, draw a line chart comparing the true value to the 

predicted value: 

 



 

236 

 
Figure 3. Line chart comparing true and predicted values after optimization of the catamaran model 

 

4. Two-factor Analysis 
Two-factor modeling analysis was performed using the 

variables Make Variant and Country/Region/State 

4.1. Single sailing catamaran 
For the variable Make Variant (manufacturer), it can be 

obtained from the analysis of the results of the F test, which 
is significant at the level, has a significant effect on Listing 
Price (USD), and has a main effect; For the variable 
Country/Region/State, it can be obtained from the analysis of 
the results of the F test that there is no significant effect on the 
level, no significant effect on the Listing Price (USD), and no 
main effect.  

4.2. Catamarans 
Due to the difference between monohulls and catamarans, 

for catamarans, the variable Make Variant (manufacturer), 
which can be obtained from the analysis of the results of the 
F test, is significant in level and has a significant effect on 
Listing Price (USD), and there is a main effect. However, for 

the variable Country/Region/State, it can be seen from the 
analysis of the results of the F test that it is significant in terms 
of level, has a significant effect on Listing Price (USD), and 
there is also a main effect.  

5. Price Forecast for Used Sailboats in 
Hong Kong 

Since the analysis methods of the two sailing boats are 
similar, we chose a single sailing catamaran as an example to 
explain the analysis process in detail. For the processing of 
data related to monohulls, it is also necessary to consider the 
impact of different regions on the listing price in order to 
predict the impact of Hong Kong characteristics on the price. 
It can be seen from the above that the linear regression model 
fits the model well, so the linear regression model is 
continued.  

5.1. Data substitution 
After multiple trainings, the fitted result plot is plotted: 

 

 
Figure 4. Fitted result plot 

 



 

237 

 
Figure 5. Histogram of feature value weights 

 
Looking at Figure 5, it can be seen that with the increase of 

training times, both the training set and the test set continue 
to converge to 60% of the fit degree. And there are no 
problems such as overfitting, and the degree of fitting is good.  

At the same time, various error indicators of linear 
regression are also calculated: the average absolute 
percentage error of the training set is 0.438, the average 
absolute percentage error of the test set is 0.351, the average 
absolute error is 66834.34542142153, and R2= 
0.4777417196056878. All the error indicators showed that the 
linear regression model had a high fit and better model 
selection. The weight of the influence of each feature value 
on the listing price in the linear regression model is obtained, 
and a histogram is plotted, as shown in Figure 5. 

Looking at Figure 5, we can see that the geographical area 
and the economic indicators within the region have almost no 

impact on the listing price, so we first find out the relevant 
economic indicators in Hong Kong, replace all other regions 
with Hong Kong, and replace all the economic indicator data 
of each region with Hong Kong data. 

5.2. Model solving 
After the data is replaced, the linear regression model is 

trained again, and the listing price in Hong Kong can be 
predicted after the training is completed. Once the predicted 
values are obtained, the regional effect of each type of sailing 
ship is analyzed. To make the results more representative, let's 
select a subset of sailboats: select a type of sailboat from each 
real region, and the selection covers all regions and all models. 
The paired-sample t-test is used below to determine whether 
there is a significant difference between the true and predicted 
values. The normality test histogram results are as follows:  

 

 
Figure 6. Normality test histogram of monohull sailboats 

 
Looking at Figure 6, it can be seen that the difference 

between the true value and the predicted value data roughly 
conforms to the normal distribution model, which can be 

approximately considered to be in line with the normal 
distribution. 

Output paired-sample t-test results: 

 

 

 



 

238 

Table 1. Monohull T test results 

Paired variable 
Mean standard deviation 

t df P 
Cohen's 

d Pairing 1 Pairing 2 
Pairing difference (pairing 

1- pairing 2) 
True_Price pairing 

simulation_HK_Price 
236513.005±157958.795 239242.583±140976.945 -2729.579±16981.851 -1.962 1298 0.050** 0.054 

Note: * * *, * *, * represent the significance level of 1%, 5% and 10% respectively 
 

The following analysis of the catamaran sailboat in the 
same square, the fitting results after linear regression training 

are as follows: 

 

 
Figure 7. Fitted result plot 

 

 
Figure 8. Normality test histogram 

 
The training set and test set continuously converged to 73% 

of the degree of fit, and the fitting results were good. The 
normality test histogram results are shown in Figure 8. The 
image roughly conforms to the normal distribution model, 

and the two-body can also be approximately considered to be 
normally distributed.  

Output paired-sample t-test results: 

 
Table 2. Catamaran T test results 

Paired variable 
Mean standard deviation 

t df P 
Cohen's 

d Pairing 1 Pairing 2 
Pairing difference (pairing 1- 

pairing 2) 
True_Price pairing 

simulation_HK_Price 
460987.855±254378.624 495198.76±215184.377 -34210.905±39194.247 -4.056 247 0.000*** 0.258 

Note: * * *, * *, * represent the significance level of 1%, 5% and 10% respectively 
 

Comparing monohulls and catamarans in the pairing 
sample T test, the pairings 1 and 2 of catamarans are about 
twice as high as those of monohulls, but the pairing difference 
of catamarans is about 12 times that of monohulls. The above 

conclusion shows that catamarans have a stronger effect than 
monohulls, and that catamarans are more susceptible to 
regional influences.  



 

239 

6. Use Pearson Correlation Analysis to 
Study the Impact of Hull 
Performance on Pricing 

From the above analysis, it can be seen that the listing price 
of the sailboat is closely related to the performance of the hull 
itself. Therefore, we will further explore the correlation 

between different properties and price, and the results can be 
used as an important basis for brokers when predicting the 
price of sailboats. Using a monohull as an example, we take 
the Pearson correlation analysis method to explore the 
correlation between market price and sailboat performance. 
Significance P>0.05 indicates a significant relationship. After 
calculating the correlation coefficient between the two 
indicators, draw the correlation coefficient heat map:  

 

 
Figure 9. Correlation coefficient heat map of monohulls 

 
Looking at the image, it can be seen that the correlation 

coefficient between the listing price and the displacement, 
length and area of the sailboat is large. The correlation 

coefficient between hull length and displacement is as high as 
0.909, which means that length determines the size of 
displacement. Plot the scatter plot of price and hull length:  

 

 
Figure 10. Scatterplot of price distribution with hull length 

 
Looking at the image, it can be seen that as the length of 

the hull increases, the price shows an upward trend; The price 
of a monohull sailboat of the same length is not much 
different.  

Also using Pearson correlation analysis, a correlation 
coefficient heat map of a catamaran sailboat is plotted: 

 



 

240 

 
Figure 11. Correlation coefficient heat map of a sailing catamaran 

 
Observing the image, it can be seen that the price of a 

catamaran is mainly affected by the sail area, length and low 
water mark, and the length is closely related to the low water 
mark. Therefore, compared to monohulls, the sail area needs 
to be considered when predicting the price.  

Scatterplot the distribution of price and hull length, and 
scatterplot of price and sail area: 

 

 
Figure 12. Scatterplot of price distribution with hull length 

 



 

241 

 
Figure 13. Scatter plot of the distribution of prices and sail area 

 
Looking at the image, it can be seen that as the length of 

the hull increases, the price shows an upward trend; As the 
sail area increases, so does the price. With a hull length 
between 38-43 feet and a sail area between 39-46 square feet, 
the price is more affordable.  

7. Model Evaluation 

7.1. Model advantages 
Based on the multiple linear regression model, the 

established model is closely related to the reality, and the 
proposed problems are solved in combination with the actual 
situation, so that the model is closer to the reality, and the 
versatility and generalization are strong. 

The model has strong operability and a wide range of 
applications, and the model based on the fourth question using 
Pearson correlation analysis is more accurate, and the 
simulation results are more reasonable. 

The model has no strict restrictions on data distribution, 
sample size and indicators, which is suitable for small sample 
data and large systems with multiple evaluation units and 
multiple indicators, which is more flexible and convenient 

7.2. Model disadvantages 
The fitting result of linear regression is about 70%, and 

there is a certain deviation between the predicted value and 
the true value. 

In the modeling process, taking a monohull as an example, 
applying the same method to a catamaran may lead to 
ignoring the particularities of the catamaran, such as finding 
that the linear regression model is not suitable for catamarans 
in the modeling process of problem one. 

References 
[1] Scientific Platform Serving for Statistics Professional 2021. 

SPSSPRO. (Version 1.0.11)[Online Application Software]. 
Retrieved from  https://www.spsspro.com . 

[2] Fisher Box, Joan. Guinness, Gosset, Fisher, and Small Samples. 
Statistical Science. 1987, 2 (1): 45–52. 

[3] Draper, N.R. and Smith, H. Applied Regression Analysis. 
Wiley Series in Probability and Statistics. 1998. 

[4] Zhou Zhihua Machine Learning [M].Tsinghua University Press, 
2016.