Question

Use the table to answer the question.

x y
0 5
2 2
3 6
4 0
7 1
Use a calculator to determine the least squares regression line for the following points. Then find the value of the y-intercept of this line. Round to the nearest hundredth, if necessary.

(1 point)
Responses

4.69
4.69

−0.59

negative 0.59

4.68
4.68

5
5

Answer 1

Compute sums: n=5, Σx=16, Σy=14, Σxy=29, Σx^2=78.

Slope m = [5(29) − 16(14)] / [5(78) − 16^2] = (145 − 224) / (390 − 256) = −79/134 ≈ −0.58955.

x̄ = 16/5 = 3.2, ȳ = 14/5 = 2.8.
Intercept b = ȳ − m x̄ = 2.8 − (−0.58955)(3.2) ≈ 4.68657 ≈ 4.69.

Answer: 4.69.