Question
Asked Jul 19, 2019
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Compute the sample correlation coefficient r for each of the following data sets and show that r is the same for both. (Use 3 decimal places.)
(i) x 8 2 9
  y 1 1 5

(ii) x 1 1 5
  y 8 2 9
  r
(i)  
(ii)  
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Expert Answer

Step 1

We know the sample correlation coefficient r between x and y variable as:

ηΣ-ΣΧΣy
wΣ-- (Σ-)Σ'-Σy
Now we can calculate the data are as follows:
2
y
X
8
1
64
2
1
4
1
2
5
81
25
45
19
7
149
27
55
ii)
n = 3
2
y
X
1
8
64
8
1
2
1
2
5
25
81
45
19
27
149
55
LO
LC
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Image Transcriptionclose

ηΣ-ΣΧΣy wΣ-- (Σ-)Σ'-Σy Now we can calculate the data are as follows: 2 y X 8 1 64 2 1 4 1 2 5 81 25 45 19 7 149 27 55 ii) n = 3 2 y X 1 8 64 8 1 2 1 2 5 25 81 45 19 27 149 55 LO LC

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Step 2

Therefore the sample correlation coefficient r between x and y for sample 1:

Σw-ΣΣ
νΣ-Σ3Σ- (Σy?
Το )
3x55-19x7
βx 149-(19)*3x27- (7)>
32
9.2736x5.6569
32
52.4594
0.6099
0.610
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Image Transcriptionclose

Σw-ΣΣ νΣ-Σ3Σ- (Σy? Το ) 3x55-19x7 βx 149-(19)*3x27- (7)> 32 9.2736x5.6569 32 52.4594 0.6099 0.610

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Step 3

Therefore the sample correlation coefficient ...

ΣΣν-ΣΣν
Υeθ)
V-Σ3ΥΣΥ-(Σ)
3x55-19x7
3x27-(73x149-(19)
32
5.6569 x9.2736
32
52.4594
= 0.6099
0.610
help_outline

Image Transcriptionclose

ΣΣν-ΣΣν Υeθ) V-Σ3ΥΣΥ-(Σ) 3x55-19x7 3x27-(73x149-(19) 32 5.6569 x9.2736 32 52.4594 = 0.6099 0.610

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