Question

Some types of algae have the potential to cause damage to river ecosystems. The accompanying data on algae colony density (y) and rock surface area (x) for nine rivers is a subset of data that come from a study.

x	49	55	50	79	44	37	70	45	50
y	154	48	24	35	36	171	13	185	27

a) Find the equation of the least squares line. (Round your answers to three decimal places.)

ŷ = __+__x

(b)What is the value of r² for this data set? (Round your answer to three decimal places.)

Write a sentence interpreting this value in context. (Round your answer to one decimal place.)

___ % of the variability in algae colony density can be explained by the approximate linear relationship between algae colony density and rock surface area.

(c) What is the value of s_e for this data set? (Round your answer to three decimal places.)

Answer 1

Excel output of regression analysis is

from the output

a)

y = -3.018X+237.6273

b)

r² = 0.319

31.9% of the variability in algae colony density can be explained by the approximate linear relationship between algae colony density and rock surface area.

c)

SE=62.491