Question

Compute the sum-of-squares error (SSE) by hand for the given set of data and linear model (5,5), (6,6), (8,9); y = x - 1. SSE =?

a) 0
b) 1
c) 2
d) 3

Answer 1

To compute the sum-of-squares error (SSE), we find the squared difference between the actual y-values and the predicted y-values. Following the given data and linear model, the SSE is calculated to be 6.

Step-by-step explanation:

To compute the sum-of-squares error (SSE), we need to find the squared difference between the actual y-values and the predicted y-values for each data point.

Given the data points (5,5), (6,6), and (8,9) and the linear model y = x - 1, we can calculate the SSE as follows:

Step 1: Calculate the predicted y-values (ū) using the linear model equation for each data point:

• ū = 5 - 1 = 4
• ū = 6 - 1 = 5
• ū = 8 - 1 = 7

Step 2: Calculate the squared difference between the actual y-values and the predicted y-values:

• (5 - 4)² = 1
• (6 - 5)² = 1
• (9 - 7)² = 4

Step 3: Calculate the sum of the squared differences:

SSE = 1 + 1 + 4 = 6

So, the SSE for the given data and linear model is 6.