A number of studies have shown lichens (certain plants composed of an alga and a fungus) to be excellent bio-indicators of air pollution. An article gives the following data (n = 13) on x = NO3 we deposition (g N/m2) and y = lichen (% dry weight): x 0.05 0.10 0.11 0.12 0.31 0.37 0.42 0.58 0.68 0.68 0.73 0.85 0.92 y0.53 0.58 0.45 0.54 0.57 0.53 1.03 0.89 0.90 1.02 0.91 1.00 1.66 Predictor Estimate Constant no3 depo 0.39329 0.9286 Standard Error 0.09566 t Stat 4.11 p-value 0.002 0.1767 5.26 0.000 s = 0.1866 R-sq 71.5% R-sq (adj) 68.9% (a) What are the least square estimates of Bo and B₁? (Round your answers to three decimal places.) bo= b₁ = (b) What is the margin of error for a 95% CI for B₁? (Round your answer to four decimal places.) Margin of Error= | (c) Predict lichen N for an NO3 deposition value of 0.7. (Round your answer to three decimal places.) % dry weight (d) What is the estimate of a? (Round your answer to four decimal places.) S= % dry weight

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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A number of studies have shown lichens (certain plants composed of an alga and a fungus) to be excellent bio-indicators of air pollution. An article gives the following data (n = 13) on x = NO3- wet
deposition (g N/m²) and y
= lichen (% dry weight):
x 0.05 0.10 0.11 0.12 0.31 0.37 0.42 0.58 0.68 0.68 0.73 0.85 0.92
y 0.53 0.58 0.45 0.54 0.57 0.53 1.03 0.89 0.90 1.02 0.91 1.00 1.66
Predictor
Constant
no3 depo
Estimate
0.39329
0.9286
0.1767
S =
0.1866
R-sq
=
71.5%
Standard Error
0.09566
t Stat
4.11
5.26
p-value
0.002
0.000
R-sq (adj)
=
68.9%
(a) What are the least square estimates of B and ẞ₁? (Round your answers to three decimal places.)
bo
=
=
(b) What is the margin of error for a 95% CI for ẞ₁? (Round your answer to four decimal places.)
Margin of Error =
(c) Predict lichen N for an NO3 - deposition value of 0.7. (Round your answer to three decimal places.)
% dry weight
(d) What is the estimate of σ? (Round your answer to four decimal places.)
S =
% dry weight
Transcribed Image Text:A number of studies have shown lichens (certain plants composed of an alga and a fungus) to be excellent bio-indicators of air pollution. An article gives the following data (n = 13) on x = NO3- wet deposition (g N/m²) and y = lichen (% dry weight): x 0.05 0.10 0.11 0.12 0.31 0.37 0.42 0.58 0.68 0.68 0.73 0.85 0.92 y 0.53 0.58 0.45 0.54 0.57 0.53 1.03 0.89 0.90 1.02 0.91 1.00 1.66 Predictor Constant no3 depo Estimate 0.39329 0.9286 0.1767 S = 0.1866 R-sq = 71.5% Standard Error 0.09566 t Stat 4.11 5.26 p-value 0.002 0.000 R-sq (adj) = 68.9% (a) What are the least square estimates of B and ẞ₁? (Round your answers to three decimal places.) bo = = (b) What is the margin of error for a 95% CI for ẞ₁? (Round your answer to four decimal places.) Margin of Error = (c) Predict lichen N for an NO3 - deposition value of 0.7. (Round your answer to three decimal places.) % dry weight (d) What is the estimate of σ? (Round your answer to four decimal places.) S = % dry weight
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