SOLUTION: The following sample observations were randomly selected. X: 4,5,3,6,10 Y: 4,6,5,7,7 a. Determine the regression equation. b. Determine the value of Ŷ when X is 7.

Algebra ->  Probability-and-statistics -> SOLUTION: The following sample observations were randomly selected. X: 4,5,3,6,10 Y: 4,6,5,7,7 a. Determine the regression equation. b. Determine the value of Ŷ when X is 7.      Log On


   

Question 766645: The following sample observations were randomly selected.
X: 4,5,3,6,10
Y: 4,6,5,7,7
a. Determine the regression equation.
b. Determine the value of Ŷ when X is 7.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The regression equation minimizes the square of the difference between the y values of the sample points and a line of the form y=a%2Ax%2Bb. Carrying out the math, this gives
a+=+%28N%2ASxy-Sx%2ASy%29%2FD
b+=+%28Sy%2ASxx-Sx%2ASxy%29%2FD
where
D=N%2ASxx-Sx%2ASx
and
N=number of samples,
Sx+= sum of x,
Sy=sum of y,
Sxx=sum of x%5E2,
Sxy=sum of x%2Ay
This gives
a=53%2F146=0.363
b=275%2F73=3.767
The value for y when x=7 is 7a%2Bb+=+921%2F146+=+6.308