Question

Following are the notations for the three sums of squares. State the name of each sum of squares and the source of variation each sum of squares represents.

a. SSE

b. SSTR

c. SST

Short answer

The notations for the three sums of squares:

a).$SSE=SSR-SSTR$.

b).$SSTR=SST-SSE$.

c).$SST=SSTR+SSE$.

Step-by-step solution

Part (a) Step 1: Given Information

Think about SSE.

Part (a) Step 2: Explanation

Treatment and error sums of squares are subtracted from the total sum of squares.

The erroneous sum of squares (SSE) is a mathematical term. It shows where the variation comes from.

$SSE=SSR-SSTR$.

Part (b) Step 1: Given Information

Think about$SSTR$.

Part (b) Step 2: Explanation

Treatment and error sums of squares are subtracted from the total sum of squares.

The treatment sum of squares is abbreviated as SSTR. It shows the source of the difference in treatment.

$SSTR=SST-SSE$

Part (c) Step 1: Given Information

Think about $SST$(Total sum of the squares).

Part (c) Step 2: Explanation

The total sum of the squares is equal to the sum of all observations plus the squared differences between them and the overall mean value.

It represents the whole variation source.

$SST=SSTR+SSE$.