Question

How do you find the sigma of the x and y values? Do you do it like a partial derivative?

Regression analysis question:

infant 1 2 3 4 5 6 7 8
birth length(in) 19.75 20.5 19 21 19 18.5 20.25 20
6-month length (in) 25.5 26.25 25 26.75 25.75 25.25 27 26.5
a researcher collected data on length of birth and length at 6 months for 8 infants.

Calculate the following values:

∑ x, ∑ x2 , ∑ y, ∑ xy, ∑ y2

Then find SSxx and SSyy

Answer 1

Explanation:

Sample size of 8 infants were taken and their birth lengths in inches recorded and also 6 months lengths.

If x is length at birth time, and y 6 month length

we have as per table below.

x y x^2 y^2 xy

1 19.75 25.5 390.0625 650.25 503.625

2 20.5 26.25 420.25 689.0625 538.125

3 19 25 361 625 475

4 21 26.75 441 715.5625 561.75

5 19 25.75 361 663.0625 489.25

6 18.5 25.25 342.25 637.5625 467.125

7 20.25 27 410.0625 729 546.75

8 20 26.5 400 702.25 530

Total 158 208 3125.625 5411.75 4111.625

`∑ x,     ∑ x2 , ∑ y,           ∑ xy,           ∑ y2\\158 208 3125.625 5411.75 4111.625`

SSxx = 3125.625 and SSyy = 5411.75