# Assignment (Doc) | Mathematics 2022

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Mathematics Assignment
Student Name:
Instructor Name:
Course Number:
27th September 2019
Meaning of correlation
This term as used in statistics is simply defined as a measure of a linear relationship between
two quantitative variables.
Two variables x and y are said to have a correlation if a change in x results into a change
in y.
Correlation and causation
Existence of a correlation between x and y doesn’t automatically mean that one event causes the
other one (Mahdavi , 2013). In other words, correlation doesn’t imply causation.
This therefore calls for further investigation to determine whether there is actual cause-effect
relationship. This is because for two correlated events x and y, there are several possible
relationships that may exist (Székely & Rizzo, 2009). This may include
i) Reverse causation
This may mean that y causes x and no the other way round (Székely & Bakirov, 2017). For
example the faster the windmills rotate, the more the wind. Faster wind velocity doesn’t imply
that wind is caused by windmills.
ii) The common causal causes both x and y
iii)There is no connection between x and y i. e the correlation is by coincidence.
Is there correlation between study time (x) and the test scores?
Illustration
The table below shows the study time in minutes and the corresponding test scores in percentage
for some student in a school who were at the same level.
We need to calculate the Pearson’s product coefficient correlation r xy.
r xy=n xy ¿ ¿ ¿
r xy= 15 ( 91405 ) ( 1055 ) (1246)
[15 ( 95075 )10552 ][15 ( 105464 )12462 ] = 13710751314530
9215972000 = 56545
95999.85 =0.589
r xy=0.589
Student Study time(minutes) Test scores
(%)
A 75 93 6975 5625 8649
B 70 77 5390 4900 5929
C 0 60 0 0 3600
D 90 89 8010 8100 7921
E 120 100 12000 14400 10000
F 105 95 9975 11025 9025
G 125 77 9625 15625 5929
H 60 71 4260 3600 5041
I 45 77 3465 2025 5929
J 120 96 11520 14400 9216
K 75 84 6300 5675 7056
L 15 69 1035 225 4761
M 50 80 4000 2500 6400
N 80 80 6400 6400 6400
p 25 98 2450 625 9604
1055 1246 91405 95075 105464
Method 2: Scatter plot
Stude
nt
Study
time(minutes)
Test scores
(%)
A 75 93
B 70 77
C 0 60
D 90 89
E 120 100
F 105 95
G 125 77
H 60 71
I 45 77
J 120 96
K 75 84
L 15 69
M 50 80
N 80 80
p 25 98

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