SSE Shortcut

[sol4bread]

CFA, Level II, Quantitative Methods/Correlation and Regression
Has anyone found a way to derive the Sum of Squared Errors with some general formula or by using the TI-BA2? Thinking that by saving time and not doing all of the tedious calculations will definitely help come crunch time! Thank you in advance for your response.
Cheers,

 

[Finkid]

sol4bread wrote:
CFA, Level II, Quantitative Methods/Correlation and Regression
Has anyone found a way to derive the Sum of Squared Errors with some general formula or by using the TI-BA2? Thinking that by saving time and not doing all of the tedious calculations will definitely help come crunch time! Thank you in advance for your response.
Cheers,

For exam, I am 99% sure they will provide us the Sum of squared errors (SSE) figure. And even if they do ask us to calculate SSE manually, then the number of observations given will be few.
The formula for SSE is = summation sign (Actual value-predicted value)^2. You will need to calculate the difference between actual values and predicted value and then square it for each observation. Finally, sum them all and you will have your SSE.
A much simpler way to calculate SSE is to deduct Regression sum of squares (RSS) from Sum of total squares (SST). But for this calculation, you will need to have values for RSS and SST.
I do have a shortcut formula for calculating the variance of Y (the dependent variable) and that is, SST divided by (n-1).
The variance of the dependent variable and SST have the same numerator so you could play with them to get one from another.

 

[sol4bread]

Thanks Finkid. I was so determined to find an answer last night that spent some time on this and came up with the following:
Sxx = Σ(x − x̅)² = Σx² − (Σx)²/n
Sxy = Σ(x − x̅)(y − y) = Σxy − (Σx)(Σy)/n
Syy = Σ(y − y-bar )² = Σy² − (Σy)²/n

Error sum of squares: SSE = (y − ˆy)² = Syy − S²xy/Sxx