What is the best estimate of the correlation coefficient of the data shown on the scatter plot?

The best estimate of the correlation coefficient of the data shown on the scatter plot is:

                            r= -0.78

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)

-12 > a

step-by-step explanation:

-11 > 1 + a

subtract 1 from each side

-11 -1> 1 -1+ a

-12 > a