Question

Given the following information, what is the least squares estimate of the y-intercept?

x y
2 55
5 75
4 80
3 85
6 99

a. 5.
b. 11.8.
c. 7.8.
d. 47.6.

Answer 1

The least squares estimate of the y-intercept is 47.6

How to get the least square estimate

From the calculated data in the attachment we have

`B_1` = 5 * 1654 - 20 * 394 / 5 * 90 - 20 * 20

= 390 / 50

= 7.8

Next we have to solve for B₀. To do this we have to get values for x and y

such that we have

mean of x = ∑x /n

= 20/5

= 4

Solve for the mean of y

y = ∑y / n

= 394 / 5

= 78.8

Next we have to use the formula

`B_0 = y -B_1x`

B₀ = 78.8 - 7.8 * 4

= 78.8 - 31.2

= 47.6

Therefore the least squares estimate of the y-intercept is 47.6