Question

Finding a Linear Regression Model
A 2-column table with 5 rows. The first column is labeled x with entries negative 4, negative 1, 0, 2, 3. The second column is labeled y with entries negative 6, negative 1, 1, 4, 7.

Find a linear function that models the data in the table.



f(x) =
x +

Answer 1

Compute the least-squares line y = mx + b.

sum x = 0, sum y = 5, sum x^2 = 30, sum xy = 54, n = 5.

m = (n·sumxy − sumx·sumy)/(n·sumx^2 − (sumx)^2) = (5·54 − 0)/(5·30 − 0) = 270/150 = 9/5.

b = (sumy − m·sumx)/n = (5 − (9/5)·0)/5 = 1.

So f(x) = (9/5)x + 1 (≈ 1.8x + 1).