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b = p * (stdDevX / stdDevY)
Y = b * X + a
1) y = -3x/4 - 2 => b1 = -3/4
2) x = -3y/4 - 7/4 => b2 = -3/4
b1 = p * (stdDevX / stdDevY)
b2 = p * (stdDevY / stdDevX)
k = (stdDevX / stdDevY)
b1 = p * k => p = b1 / k
b2 = p / k => 1/k = b2 / p
p = b1 * b2 / p => p*p = b1 * b2
p*p = (-3/4) * (-3/4) = 9/16
p = 3/4
b1 and b2 are negative,
so Pearson Coefficient is -3/4
In a simple linear regression with 1 independent variable 'x', B1 (coefficient of x in the regression equation) is equal to
where r is the Pearson correlation coefficient.
So given that B1 is the same for both regression equations, we know that the ratio stdx/stdy must be the same, since r is the same value in both equations. (r is the correlation between x and y). And then as a direct result, we get r = B1.
I would like to complete the 10 days of statistics, but I am locked out from reattempting the multiple choice question. I got the question wrong on my first attempt and then frustratingly guessed the answer knowing that my odds of correctly guessing the answer within the allotted number of guesses were 5/6. Unfortunately, I guessed wrong everytime. I know guessing is not the way to go and would like the challenge to be reset if possible. I can't stand having this challenge hanging at 96% on my front page. What can I do?!
By rearranging the equations we can see that y ~-x. So that eliminates all the positive choices. Correlation is on the range [-1 1] so we can eliminate -4/3 and they are not perfectly correlated (because then the two equations would be equal). So by elimination the answer must be the one that is negative and >-1