Question 766645
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*x+b}}}. Carrying out the math, this gives

{{{a = (N*Sxy-Sx*Sy)/D}}}
{{{b = (Sy*Sxx-Sx*Sxy)/D}}}

where

{{{D=N*Sxx-Sx*Sx}}}

and 
{{{N}}}=number of samples, 
{{{Sx }}}= sum of {{{x}}}, 
{{{Sy}}}=sum of {{{y}}}, 
{{{Sxx}}}=sum of {{{x^2}}}, 
{{{Sxy}}}=sum of {{{x*y}}}

This gives

{{{a=53/146=0.363}}}
{{{b=275/73=3.767}}}

The value for {{{y}}} when {{{x=7}}} is {{{7a+b = 921/146 = 6.308}}}