Answer:
Step-by-step explanation:
Hello!
The coefficient of correlation: r
It takes values between -1 and 1
This coefficient gives an idea of the degree of correlation between the variables.
If ρ = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is cero
If ρ < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.
If ρ > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)
The closer to 1 or -1 the coefficient is, the stronger the association between variables. Using the absolute value of the correlation coefficients you can compare them, the greater the value, the stronger is the association between variables. For example, if you were to have two coefficients r₁= -0.24 and r₂= 0.67 then the absolute values are Ir₁I= 0.24 and Ir₂I= 0.67 you can see that the coefficient of the second sample is bigger than the first sample, that means that there is a stronger correlation in the second sample than the first one.
Lets consider the following values for r:
Example 1
A. r₁= 0.6
B. r₂= -0.55
C. r₃= 0.4
D. r₄= -0.25
To compare these correlation coefficients you have to compare their absolute values
|r₁|= |0.6|, |r₂|= |0.55|, |r₃|= |0.4|, |r₄|= |0.25|
Now you order them from least to greatest:
|r₄|= |0.25|, |r₃|= |0.4|, |r₂|= |0.55|, |r₁|= |0.6|
⇒ The coefficient that represents the weakest correlation is r₄= -0.25
Example 2
A. r₁= 0.5
B. r₂= -0.35
C. r₃= 0.3
D. r₄= -0.45
Same as before, you have to work with the absolute values:
|r₁|= |0.5|, |r₂|= |0.35|, |r₃|= |0.3|, |r₄|= |0.45|
And order them from least to greatest:
|r₃|= |0.3|, |r₂|= |0.35|, |r₄|= |0.45|, |r₁|= |0.5|
⇒ The coefficient that represents the weakest correlation is C. r₃= 0.3
I hope this helps!
