The Marseille Water Taxi ferries tourists from the harbor at Marseille, France,
ID: 2907254 • Letter: T
Question
The Marseille Water Taxi ferries tourists from the harbor at Marseille, France, to the Frioul Islands in the Mediterranean Sea. The table below shows the number of passengers on the noontime ferry over seven randomly selected days along with the current ambient temperature in degrees Celsius.
Temperature
Passengers
16
15
19
20
22
20
26
22
18
10
24
18
Use the Marseille Water Taxi data to
A) determine the correlation coefficient for this data and
B) interpret its meaning.
Temperature
Passengers
16
15
19
20
22
20
26
22
18
10
24
18
Explanation / Answer
Variables: Temperature(x) Passengers
(y)r = n ?xy – (?x)(?y) / ?[n ?x2 – (?x)2] [ n ?y2 – (?y)2
]n = 6
?x = 16+19+22+26+18+24 = 125
?y = 15+20+20+22+10+18 = 105
?xy= (16*15) +(19*20)+(22*20)+(26*22)+(18*10)+(24*18) = 2244
?x2 = 256+361+484+676+324+576 = 2677
?y2 = 225+400+400+484+100+324= 1933r =(6*2244) – (125*105) / ?[(6*2677)-15625)] *[(6*1933)-11025)]= 339/500.4= 0.6775
Therefore the correlation coefficient is 0.677, which means it is a moderately positive correlation and it also means that y tends to increase as x increases.
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