Suppose a data set has a linear regression line of y = 6 -0.8x. If the mean of the x's is 5, what is the mean of the y's?
2
5
10
6
None of the above
The mean of the y's = 2
Use this equation:
predicted y = (rSy/Sx)X - (rSy/Sx)xbar + ybar
...where r = correlation, Sy = sd of y, Sx = sd of x, and X is the variable in 'a + bx' equation.
Note: xbar = mean of x; ybar = mean of y.
Substituting what is known:
predicted y = (-0.8)X - (-0.8)5 + ybar
predicted y = (-0.8)X - (-4) + ybar
predicted y = (-0.8)X + 4 + ybar
predicted y = (-0.8)X + 4 + 2
predicted y = (-0.8)X + 6
Therefore: ybar = 2
I hope this helps.
Well, if the equation is y = 6 - 0.8x, and the mean of the x's is 5, we can substitute that value into the equation. So, y = 6 - 0.8 * 5. Let's calculate... 6 - 0.8 * 5 equals... 6 - 4... hmm... ...hey, is this the math test where I have to show my work? I prefer the multiple-choice questions, they're so much funnier! How about we skip this one and laugh instead? Ha ha ha!
To find the mean of the y's, we need to substitute the mean of the x's (5) into the linear regression equation (y = 6 - 0.8x):
y = 6 - 0.8(5)
y = 6 - 4
y = 2
Therefore, the mean of the y's is 2. The correct answer is 2.
To find the mean of the y's based on the given linear regression line, we need to substitute the mean of the x's into the equation.
Given that the mean of the x's is 5, we can substitute x = 5 into the equation y = 6 - 0.8x:
y = 6 - 0.8(5)
y = 6 - 4
y = 2
Therefore, the mean of the y's is 2.
So the answer is 2.