import math

byx = -3/4 bxy = -3/4

result = math.sqrt(byx*bxy)

print(round(-1*result, 2))

for every time that we have a positive correlation coefficient, the slope of the regression line is positive.

in the formula a = r(sy/sx) since sy and sx will always be +ve a will have same sign as corr. coeff.

A useful piece of information is the definition of b_xy—this is the slope of the regression line resulting from regressing x on y.

I found Wikipedia's "geometric interpretation" to be helpful here, i.e. r² = 1/cos(delta) - tan(delta) where delta is the angle between the given regression lines. https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient#Geometric_interpretation

(Delta is easy to calculate from the y = f(x) = ax + b form of both regression lines, as a = tan(alpha) where alpha is the angle of the function w.r.t. the x axis)

Personal pitfalls: forgetting to get the square root, forgetting to consider the sign (+ or -) of the result.

The way to use simulation is adding information to the problem. I think the key point to this question is to understand the math behind linear regression and the Peason correlation. From the problem statement, we know that y= -3/4*x-2 +e (1); and x=-3/4*y -7/4 +e (2). The linear regression coefficient beta is Sxy/Sxx ( in y=beta*x+e format), where S regresents (summation of the difference.....please check the linear regression lecture notes). So, applying the regular beta formular to our problem, we get Sxy/Sxx= -3/4 from (1) ......(3); and Syx/Syy=-3/4 from (2) ........(4); Recall that the Peason corelation is: r=Sxy/(sqrt(Sxx)*sqrt(Syy)) Here Sxy=Syx. So, if we multiply (3) and (4) and sqrt the result, we get: sqrt(Sxy*Syx/(Sxx*Syy))=r=+ or - 3/4. Since y and x are negtive corellated based on the negative beta, we get the r = -0.75.

Please excuse me if there are some types.

I don't see why this isn't 0.96, I get the angle as 16.26 with a cos of 0.96.