To find the equation of the least-squares regression line, you can use the formula:
hat y = b + r(s_y/s_x)(x - overline x)
Plugging in the given values:
b = s_y - r(s_y/s_x)overline x
= 7 - 7(7/13.5)(13.5)
= 7 - 3.7(13.5)
= 7 - 50.04
= -43.04
Therefore, the equation of the least-squares regression line is:
hat y = -43.04 + 3.7(x - 13.5)
hat y = -43.04 + 3.7x - 50.45
hat y = -50.45 + 3.7x
So, the closest option is:
A. hat y = -51.52 + 1.26x
We have a bivariate data set and compute the following: r = 7, s_{y} = y s_{x} = b overline x = 13.5 , overline y =51 . We want to know the equation of the least-squares regression line, but we don't have a calculator that's powerful enough to do the necessary computations. Determine the equation of the least-squares regression line from the given data.
A. hat y = - 51.52 + 1.26x
B. dot y = 46.34 + 0.39x
C. overline y = - 6.624 + 39x
D. hat y = 34.59 + 1.26x
E. You can't compute the regression line without knowing the original data.
1 answer