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 49 79 44 37 71 45 48
y 152 48 20 35 40 171 15 185 25
(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
se
for this data set? (Round your answer to three decimal places.)
Write a sentence interpreting this value in context.
All observations are exactly 2se from the least squares regression line.Observations tend to deviate from the least squares regression line by the value of 2se typically. All observations are exactly se from the least squares regression line.Observations tend to be se below the least squares regression line on average.Observations tend to deviate from the least squares regression line by the value of se typically.
(d)
Is the linear relationship between rock surface area and algae colony density positive or negative? Is it weak, moderate, or strong? Justify your answer.
The relationship between rock surface area and algae colony density is ---Select (positive OR negative)--- positive negative because the slope of the regression line is ---Select (positive OR negative) --- positive negative . The relationship is ---Select--- (weak (|r| < 0.5) OR moderate (0.5 < |r| < 0.8) OR strong (|r| > 0.8) )