Question
Asked Sep 21, 2019
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is finding a linear correlation coefficient the same as finding the correlation coefficient? if not, an example of linear correlation coefficient would help.

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Expert Answer

Step 1

The type of coefficient to be calculated would depend on whether the variables are categorized as nominal, ordinal or interval data. When both variables are nominal, for an instance, Phi ecefficient is used. When both variables are ordinal Spearman Rank correlation coefficient is used.

For linear relationship, Pearson product-moment correlation coefficient is used. This correlation coefficient gives us an idea about the linear relationship between the two variables. Correlation coefficient is loosely used in texts to mean Pearson product-moment correlation coefficient.

The formula for calculating this correlation coefficient is:

Σx-ΣΙΣ.
inΣ- (ΣΟΣΥ- (Σ)1
Where
n number of pairs of observations
Zxy ILm of the prodncts of paired scores
Exsum ofx scores
Ey sum ofy scores
Ex2-SLm of squared x scores
Ey m of squared y scores
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Σx-ΣΙΣ. inΣ- (ΣΟΣΥ- (Σ)1 Where n number of pairs of observations Zxy ILm of the prodncts of paired scores Exsum ofx scores Ey sum ofy scores Ex2-SLm of squared x scores Ey m of squared y scores

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Step 2

Now let's consider an example:  suppose we have 6 individuals and we want to see how the age of these individuals is related with their glucose level. The data is given below:

Glucose level y
Age x
42
99
22
65
24
79
43
75
40
87
59
81
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Glucose level y Age x 42 99 22 65 24 79 43 75 40 87 59 81

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Step 3

Now we can find the correlation coefficient for the given dat...

Glucose level y
xy
Age x
42
99
1764
9801
4158
4225
1430
22
65
484
24
79
576
6241
1896
1849
43
75
5625
3225
40
87
1600
7569
3480
59
81
3481
6561
4779
Σν 486
Σν'-
Σ-
Ex 230
40022 >xy=18968
= 9754
6x18968-230 x 486
V16x9754-2307][6x40022-436*]
113808-111780
|(58524-52900)240132- 236196)
2028
22136064
2028
4704.898
Tounded to 3 decimal places
-0.431
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Glucose level y xy Age x 42 99 1764 9801 4158 4225 1430 22 65 484 24 79 576 6241 1896 1849 43 75 5625 3225 40 87 1600 7569 3480 59 81 3481 6561 4779 Σν 486 Σν'- Σ- Ex 230 40022 >xy=18968 = 9754 6x18968-230 x 486 V16x9754-2307][6x40022-436*] 113808-111780 |(58524-52900)240132- 236196) 2028 22136064 2028 4704.898 Tounded to 3 decimal places -0.431

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