Question

When r = 0, the best estimate of variable Y from a known variable X is…

a.            the standard deviation of X

b.            the standard deviation of Y

c.            Mean of X

d.            Mean of Y

Answer 1

Linear regression equation is - Y = b0 + b1X.

Where, b0 = $\bar{y} - b_{1}\bar{x}$ & b1 = $r\tfrac{s_{y}}{s_{x}}$

Here, given that r = 0.

So, it implies that value of b1 also becomes 0.

Now, we have b0 = $\bar{y} - b_{1}\bar{x}$ = $\bar{y}-0(\bar{x})$ = $\bar{y}$

Hence, linear regression equation becomes as -

Y = b0 + 0(X)= b0 = $\bar{y}$ ........ ( since, b1 = 0)

Hence, best estimate of variable Y from known variable X is mean of y.

Option D is correct.