Answer:
The best estimate of the correlation coefficient of the data shown on the scatter plot is:
r= -0.78
Explanation:
We know that the correlation coefficient determines the strength between the two variables.
Also, if the correlation coefficient is negative then the variables have a negative association
(i.e. with the increase of one variable the other variable decreases )
And the correlation coefficient is positive if the variables have a positive association i.e. with the increase/decrease of one variable the other variable also increases/decreases.
Also, if the correlation coefficient is close to 0 then the variables have no association and if the correlation coefficient has a absolute value close to 1 then they have a strong association.
Here by looking at the scatter plot we see that when we draw a decreasing trend line then the data points will be closely related to line also the association is negative because with the increasing x-variable the y-variable is decreasing.
Hence, the best possible option is:
r= -0.78
( a) r=0.78 this option is incorrect as r is positive.
b) r= -0.2 this option is incorrect as r is close to 0 which means the variable has no association but they have a linear negative association.
c) r= 0.2 again r value is positive which is not possible here)