Question

Is it true that total sample variation of the dependent variable Y, also called the total sum of squares = (s^2)y * (n − 1) where n = sample size and s^2y is the sample variance of Y? Why or why not?

Answer 1

We know that , total sum of squares of the dependent variable Y = (Y - )2 , where is the mean.

Also, the sample variance of Y , s2Y = (1/n-1)(Y - )2

From this equation , we get , (Y - )2 = s2Y *(n-1)

i.e , total sum of squares = s2Y *(n-1)

Hence proved.