Respuesta :
Answer:
A. 0.827
Step-by-step explanation:
Correlation Coefficient(r) shows the direction and strength of relationship between two variables.
The formula used to calculate correlation is:
[tex]Correlation(r) = \frac{Cov(x, y)}{\sigma_{x}\sigma_{y}}= \frac{E(x-\mu_{x})(y-\mu_{y})}{\sigma_{x}\sigma_{y}}[/tex]
where, Cov(x,y) = Covariance of x and y
[tex]\mu_{x} [/tex] = mean of x
[tex]\mu_{y} [/tex] = mean of y
[tex]\sigma_{x} [/tex] = standard deviation of x
[tex]\sigma_{y} [/tex] = standard deviation of y
and, E = Expectation.
Now, we have data: Shelf Space(x) : (5,5,5,10,10,10,15,15,15,20,20,20)
Weekly Sales(y): (1.6, 2.2, 1.4, 1.9, 2.4, 2.6, 2.3, 2.7, 2.8, 2.6, 2.9, 3.1)
Mean of x = 12.5
Mean of y = 2.375
Standard deviation of x = 5.84
Standard deviation of y = 0.522
Covariance of x and y = 2.52
Putting all values, We get
Correlation Coefficient = 0.827
The correlation coefficient lies between -1 to +1.
As the increase in the value of one variable also increases the value of other variables is called positive correlation. Also, the value of positive correlation lies between 0 to 1.
And decrease in the value of one variable, increases the value of other variables is called negative correlation. Also, the value of negative correlation lies between -1 to 0.
