Answer:
a) ρ (X,Y) = 0.125
b) The linear relationship is weak because ρ (X,Y) is almost 0
c) There is a positive linear relationship because ρ (X,Y) > 0
Step-by-step explanation:
The Pearson correlation coefficient is calculate as :
ρ (X,Y) = (σXY) / (σX)(σY)
-1 ≤ ρ ≤ 1
When ρ = 0 there is no linear relationship between the variables. This does not mean that the variables are independent.
When ρ = 1 the linear relationship is perfect positive. ρ = 1 means a direct relation between X and Y : When X increases also Y increases in constant proportion. When Y increases also X increases in constant proportion.
When ρ = -1 the linear relationship is perfect negative. ρ = -1 means a inverse relation between X and Y : When X increases Y decreases in constant proportion. When Y increases X decreases in constant proportion.
In our exercise ρ (X,Y) = 13.44 / (15.57)(6.90) = 0.125
a) ρ (X,Y) = 0.125
b) The linear relationship is weak because ρ (X,Y) is almost 0
c) There is a positive linear relationship because ρ (X,Y) > 0
