For the regression model yi = 0+1 xi + i , the residuals are defined as ei = yi 0 1 xi ,

For the regression model yi = β0+β1xi+εi, the residuals are defined as ei =yi − ˆβ0 −ˆβ1xi, where ˆ β0and

ˆ β1 are the least squares estimates.

a. show that the least squares estimate of the slopeˆ β1 is also equal to

b. show that the least squares estimate of the slopeˆ β1 is also equal to

c. show that the sum of the residuals is always equal tozero, i.e   
 
 

B || 2(-x)(-) 2 (1-1)- 2