week 2 - equations

Question 1

What equation do you use to work out total variation?

Answer 1

SST = SSR + SSE

Total Sum of Squares = Regression Sum of Squares + Error Sum of Squares

Question 2

How do you work out SST (Total Sum of Squares)?

Answer 2

SST = ∑(Yi - ȳ)^2

Question 3

How do you work out SSR (Regression Sum of Squares)?

Answer 3

SSR = ∑(Ŷi - ȳ)^2

Question 4

How do you work out SSE (Error Sum of Squares)?

Answer 4

SSE = ∑(Yi - Ŷi)^2

Question 5

What is the equation for R^2 (the Coefficient of Determination)?

Answer 5

R^2 = SSR / SST = regression sum of squares / total sum of squares

–> R^2 = ∑(Ŷi - ȳ)^2 / ∑(Yi - ȳ)^2

Question 6

What is the equation for the Standard deviation of the variation of observations around the regression line?(What does Syx = ?)

(What does Syx = ?)

Answer 6

Syx = √(SSE / n-2) = √(∑(Yi - Ŷi)^2 / n-2)

where SSE = error sum of squares
n = sample size