Question

A 2-column table with 6 rows. The first column is labeled week with entries 1, 2, 4, 6, 8, 10. The second column is labeled miles run with entries 5, 8, 13, 15, 19, 20.
Rita is starting a running program. The table shows the total number of miles she runs in different weeks.

What is the equation of the line of best fit for the data? State each number to the thousandths place.

y ≈
x +

Answer 1

Compute the least-squares slope and intercept:

n = 6, Σx = 31, Σy = 80, Σxy = 515, Σx^2 = 221.

m = (nΣxy − ΣxΣy)/(nΣx^2 − (Σx)^2) = (6·515 − 31·80)/(6·221 − 31^2) = 610/365 ≈ 1.671
b = (Σy − mΣx)/n = (80 − 1.671·31)/6 ≈ 4.689

So the line of best fit is:
y ≈ 1.671 x + 4.689