Question

Please show your work. God bless

1. (40 points) Consider the following five observations. (9 points) (x-x) (x - x) (y- y) (x - x)(y-y) 2*- {x = 1012 (-:-)= {(x - 1)2 = 20;-)) = (x x)(y- » a) (6 points) What are the sample means of x and y? b) Complete the entries in the table above. Put the sums in the last row. (Show work below) c) Calculate Bo and write out the equation for the fitted sample regression line (.e.) - ...) where Bo and B. are replaced by their actual values, interpret Bo and B1. d) Use the least squares estimates from part (c) to complete the table below. Show your work below.

Answer 1

a) sample mean of x, x̄= Σx/n = 10/5 = 2
  sample mean of y, ȳ = Σy/n = 12/5 = 2.4

b)

x	y	(x-x̄)	(x-x̄)2	(y-ȳ)	(y-ȳ)2	(x-x̄)*(y-ȳ)
0	6	-2	4	3.6	12.96	-7.2
1	2	-1	1	-0.4	0.16	0.4
2	3	0	0	0.6	0.36	0
3	1	1	1	-1.4	1.96	-1.4
4	0	2	4	-2.4	5.76	-4.8
Σx =	Σy =	Σ(x-x̄) =	Σ(x-x̄)2 =	Σ(y-ȳ) =	Σ(y-ȳ)2 =	Σ (x-x̄)(y-ȳ) =
10	12	0	10	0	21.2	-13

c) b₁ = Σ (x-x̄)(y-ȳ) / Σ(x-x̄)² = -13/10 = -1.3
b₀ = ȳ - b₁x̄ = 2.4 - (-1.3*2) = 5
thus ŷ_i = 5 -1.3*x_i

d)

x	y	ŷi = 5 -1.3*xi	êi = yi-ŷi
0	6	5	1
1	2	3.7	-1.7
2	3	2.4	0.6
3	1	1.1	-0.1
4	0	-0.2	0.2