Fishing Boat Equipment and Skipper Experience

This assignment analyzes the relationship between general equipment level and skipper experience for 151 fishing boats deployed in Tasmania. It investigates if boats with above-average equipment also have experienced skippers and calculates the number of boats across different combinations of equipment and experience levels. Additionally, the assignment examines the relationship between time spent at sea and catch value specifically for boats with experienced skippers, employing statistical methods like Pearson correlation coefficient and regression analysis to determine the strength of this relationship.

Quantitative Methods
BEA140
Student id
[Pick the date]

Analysis of the general equipment type and experience of skippers for boats
Aims
 To determine if the boats having the above average general equipment also had
experienced skippers.
 To determine the number of boats for various possible combinations of general
equipment level and also experience level.
Background
Information was collected for the fishing catch of 151 boats deployed in Tasmania. For each of
these boats, data was collected about the skipper being experienced or not along with the general
level of equipment used (average or above average).
Findings
 For boats having above average general equipment, it cannot be concluded that they had
experienced skippers (Table 1)
 There were 20 boats with above average general equipment and inexperienced skipper.
There were 53 boars with above average general equipment and experienced skipper.
There were 26 boats with average general equipment and inexperienced skipper. There
were 52 boars with average general equipment and experienced skipper.
Statistical Method and Result
 Computational Methods
Equipment – General level of fishing gear (average OR above average), Experience of Skipper
The requisite table to determine the number of boats there with each combination of the
experience and general equipment type is computed based on Pivot Table tool of excels and is
shown below (Table 1).
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Relationship between time spent at sea and catch value for boats having experienced
skippers
Aim
To determine the relationship between the time spent at sea and the value of the catch for those
specific boars that have experienced skippers.
Background
Data has been collected for randomly selected 151 boats that are working in Tasmania. Also, the
value (i.e. price paid for catches in $ 000’s) along with the time spent at sea (hours) was
recorded.
Findings
 There is very low correlation between the time spent at sea and the value of catch for
boats with experienced skippers. Hence, the value of catch would be driven by various
other factors except time spent at sea by experienced skippers (Figure 1)
 The predicted value of catch for the time spent at sea by experienced skipper is
yc=63.98+0.0667 x
Statistical Method and Result
 Computational Methods
The value of “Pearson correlation coefficient” is computed based on the formula shown below:
r =(∑ xy −∑ x ∑ y
n )/ √(∑ x¿¿ 2− (∑ x )2
/( n))−(∑ y ¿¿ 2− ( ∑ y )2
/n) ¿ ¿
Independent variable x = Time
Dependent variable y = Value
Number of observation n=105
 Pearson correlation coefficient
r =(811639−11405∗7422
105 )/( √(1327471)− ( 11405 )2 /(105)¿−(549474)− ( 7422 )2 /105)¿)
2

r = 5468.429
46936.04
r =0.1165
 The regression line yc=a+bx
The value of coefficients a∧b is computed based on the given formulas.
b= ( n∑ xy −∑ x ∑ y )
n(∑ x ¿¿ 2)− ( ∑ x )
2
¿
¿ ¿ ¿
b=0.06167
a=∑ y−b ∑ x
n
¿ ( 7422− 0.0667∗11405
105 ) ¿ 63.98
The regression line yc=a+bx or yc=63.98+ 0.0667 x
 Standard error of the estimates would be computed based on the formula given below:
se
2=∑ ¿ ¿ ¿
The value of ycwould be determined based on the regression line for given values of x.
∑ ¿¿
n−2=105−2=103
se
2= 24507.38
103 =$ 237.94
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 Coefficient of determination (r2 )
r2= SSR
SST
Where,
 SSR=∑ ¿ ¿
y=Mean value=70.69
∑ ¿¿
Hence, SSR=∑ ¿ ¿
Now,
 SST =∑ ¿ ¿
r2= SSR
SST = 337.24
24844.63 =0.01357∨0.0136
 Scatter plot between the variable value and time is shown below:
40 60 80 100 120 140 160 180 200
0
20
40
60
80
100
f(x) = 0.061671158045332 x + 63.9870518332666
R² = 0.0135741342124951
Scatter Plot
Time (Total time on trips (hours))
Value (Price paid for catches
($1,000))
Figure 1: Clearly the linear relationship between the two variables of interest is very weak which
is also highlighted by the low coefficient of determination.
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