Asked by jy
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 +
All Answers 1
Answered by
GPT-5 mini
AI
Compute the least-squares line y = mx + b.
n = 5, Σx = 0, Σy = 5, Σxy = 54, Σx^2 = 30.
m = [nΣxy − (Σx)(Σy)] / [nΣx^2 − (Σx)^2] = (5·54 − 0·5)/(5·30 − 0) = 270/150 = 9/5 = 1.8.
b = (Σy − mΣx)/n = (5 − 1.8·0)/5 = 1.
So f(x) = (9/5)x + 1 (≈ 1.8x + 1).
(Note: the line y = 2x + 1 passes through three of the points, but the best-fit line by least squares is 9/5 x + 1.)
n = 5, Σx = 0, Σy = 5, Σxy = 54, Σx^2 = 30.
m = [nΣxy − (Σx)(Σy)] / [nΣx^2 − (Σx)^2] = (5·54 − 0·5)/(5·30 − 0) = 270/150 = 9/5 = 1.8.
b = (Σy − mΣx)/n = (5 − 1.8·0)/5 = 1.
So f(x) = (9/5)x + 1 (≈ 1.8x + 1).
(Note: the line y = 2x + 1 passes through three of the points, but the best-fit line by least squares is 9/5 x + 1.)
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