Question

Consider the following data:

x	1	2	3	6
y	6	5	4	1
`bb(x - bar(x))`
`bb(y - bar(y))`

1. Calculate `bar(x)` and `bar(y)`   [1]
2. Complete the table.   [1]
3. Calculate b_xy   [1]

Answer 1

a. `bar(x) = (1 + 2 + 3 + 6)/4`

= `12/4`

= 3

`bar(y) = (6 + 5 + 4 + 1)/4`

= `16/4`

= 4

b.

x	y	`bb(x - bar(x))`	`bb(y - bar(y))`
1	6	1 – 3 = –2	6 – 4 = 2
2	5	2 – 3 = –1	5 – 4 = 1
3	4	3 – 3 = 0	4 – 4 = 0
6	1	6 – 3 = 3	1 – 4 = –3

c. `b_(xy) = (sum_(i = 1)^4 (x_i - bar(x))(y_i - bary))/(sum_(i = 1)^4 (x_i - x)^2)`

= `((-2)(2) + (-1)(1) + (0)(0) + (3)(-3))/((-2)^2 + (-1)^2 + (0)^2 + (3)^2)`

= `(-4 - 1 - 9)/(4 + 1 + 9)`

= `(-14)/14`

= –1

b_xy = –1.