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.

Answer 1

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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