Page: 8 prev next 






Special Cases of Least Squares











For each type of linear problem, there are
special cases in which the LS estimates simplify to
give familiar formulas. 














    

  1. 1.  y(i) = beta(0) + e(i)

    

      

    • beta hat(0) = 1/n sum[i=1 to n] y(i)


      

    

  2. 2.  y(i) = beta(0) + beta(1)x(i) +e(i)

    

      

    • beta hat(1) = (sum[i=1 to n](x(i) - xbar)(y(i) - ybar)) / (sum[i=1 to n] (x(i) - xbar)^2)

      

    • beta hat(0) = ybar - beta hat(1) xbar


      

    

  3. 3.  y(ij) = mu +tau(i) + e(ij), sum[tau(i) = 0]

    

      

    • beta hat(o) = ybar..

      

    • beta hat(i) = ybar(i). - ybar..,  i >0