Question

The following information regarding a dependent variable Y and an independent variable X is provided

n = 4

ΣX = 90

ΣY = 340

Σ (Y - )(X - ) = -156

Σ (X - )2 = 234

Σ (Y - )2 = 1974

SSR = 104

The sum of squares due to error (SSE) is?

Answer 1

Answer 2

Let's break down the problem and find the sum of squares due to error (SSE).

Given Information:

• n = 4 (Number of data points)

• ΣX = 90 (Sum of X values)

• ΣY = 340 (Sum of Y values)

• Σ(Y - Ȳ)(X - <0xC8><0xB3>) = -156 (Sum of cross-products of deviations)

• Σ(X - <0xC8><0xB3>)² = 234 (Sum of squared deviations of X)

• Σ(Y - Ȳ)² = 1974 (Sum of squared deviations of Y)

• SSR = 104 (Sum of squares due to regression)

Goal:

Find SSE (Sum of squares due to error).

Relationship:

We know that the total sum of squares (SST) is the sum of the sum of squares due to regression (SSR) and the sum of squares due to error (SSE):¹

SST = SSR + SSE

We are given SSR, so we need to find SST to calculate SSE.

Calculating SST:

SST is the sum of squared deviations of Y from its mean (Ȳ):

SST = Σ(Y - Ȳ)²

We are given that Σ(Y - Ȳ)² = 1974.

Therefore, SST = 1974.

Calculating SSE:

Now we can use the relationship SST = SSR + SSE to find SSE:

SSE = SST - SSR

SSE = 1974 - 104

SSE = 1870

Answer:

The sum of squares due to error (SSE) is 1870.