Question

Which of the following lines would be the best fit for the data points plotted in the scatter plot below?

The scatter plot on graph showing the points (1, 4), (2, 5), (3, 4), (4, 6), (5, 5), (6, 6), (6, 8), (7, 7), (8, 7), and (8, 8).
A.
y
=
0
.
5
x
−
3
.
4

B.
y
=
0
.
5
x
+
3
.
4

C.
y
=
3
.
4
x
−
0
.
5

D.
y
=
3
.
4
x
+
0
.
5

Answer 1

Compute the line of best fit (least squares).

Mean x = 50/10 = 5, mean y = 60/10 = 6.
Slope = sum[(xi−5)(yi−6)] / sum[(xi−5)^2] = 28 / 54 ≈ 0.5185.
Intercept = 6 − 0.5185·5 ≈ 3.41.

So the best-fit line is about y ≈ 0.52x + 3.41, which matches choice B: y = 0.5x + 3.4.