Question

Suppose the line of best fit for some data points has a slope of 2.334. If the mean of the x-coordinates of the data points is 6.607, and the mean of the y-coordinates is 10.738, what is the y-intercept of the line to three decimal places?

Answer 1

-4.683

















apex, apex, apex, apex

Answer 2

The y-intercept of the line is −4.683.

Explanation:

Given information: Slope = 2.334,
`\overline{x}=6.607` and
`\overline{y}=10.738`.

The general equation of line of best fit is

`y=a+bx`

where, a is y-intercept and b is slope.

`b=\frac{\sum_(i=1)^nx_iy_i-n\overline{x}\overline{y}}{\sum_(i=1)^nx_i^2-n\overline{x}^2}`

`a=\overline{y}-b\overline{x}`

We need to find the value of y-intercept (value of a).

Substitute
`\overline{x}=6.607`,
`\overline{y}=10.738` and b=2.334 in the above equation.

`a=10.738-2.334(6.607)`

`a=10.738-15.420738`

`a=-4.682738`

`a\approx -4.683`

Therefore the y-intercept of the line is −4.683.