If the correlation coefficient turns out to be a relatively high value, then the value of y1 will be

Question

a.) Relatively low

b.) Relatively high

c.) Unrelated to the value of r

d.) Low if r is positive and high if r is negative

 

I want to say the answer is b, but I'm not entirely sure.

Answer 1

Tayllor,

 

I don't know what y1 is?  But this may help you pick the right answer.

 

If two variables x & y are highly correlated, then the change in one will "explain" most of the change in the other. If r, the correlation coefficient is positive, then they both go in the same direction: a positive change in one produces a positive change in the other, and a negative change produces a negative change.  If r is negative, however, then the changes in x and y go in opposite directions.

 

Think of a straight line y = mx + b.  Then Δy = m (Δx)  as Δb = 0 since it is constant.  Now, if a bunch of data points are plotted on graph paper, and they appear to be "close" to a straight line (like say within the chalk area as the chalk is held sideways and slid across the blackboard), then r is pretty high. And depending on whether m is positive or negative, the delta formulation shows you how the changes go.  BTW, if all the data points lie exactly on the line, then correlation is 1.

 

If however the plotted points are like a bloated elliptical cloud, then r is low since you can't fit a reasonable straight line to that data smear other than the tilt of the major axis of that elliptical blob. That tilt tells you that whatever little correlation exists tend to be slightly positive or negative, but the low correlation also tells you that change in either variable explains very little of the change in the other.