the ans is -3/4

I am confused how the pearson correlation can be calculated by finding the slope and the editorial did not make sense entirely to me. The formula for r:

r=∑((Xi−Xmean)*(Yi−Ymean)) / sqrt(∑((Xi−Xmean)^2) sqrt((Yi−Ymean) ^2)

and the formula for calculatin a slope: b = ∑((xi−Xmean)(yi−Ymean))/ ∑(xi−Xmean) so how is it possible to calculate r without knowing all this?

You have 5 attempts and You have 6 answers. Considering that 2 answers do not correspond to the range of Pearson Correlation Coefficient, you have 4 answers and 5 attempts.

I am confused with the question. I understand it is testing the relationship between slope coefficinet and pearson correlation coefficient. The anwers is to calculate the 2 pearson correlation coefficients from the two regressions separately. Then taking a square root on the product of the two values. We get the final answer. But what does this value really mean here? The strength and direction between two regressions? or the weighted pearson coefficient from the two regression?

The PCC is definitely negative because:

3x + 4y + 8 = 0;
y = -2 - 3/4x;
a = -2;
b = -3/4 = p * sigmaY / sigmaX;

sigmaY and sigmaX are positive then p is negative.

• It cannot be -1 because regression line is sloping.
• It cannot be -4/3 because PCC = [-1;1].
• -3/4 is the correct answer.