best fit lines & scientific hypotheses. bellringer question what is the y-intercept and slope of...
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Best Fit Lines &Scientific Hypotheses
Bellringer question
• What is the y-intercept and slope of this line?
-4 -3 -2 -1 0 1 2 3 4 5 6
-1
0
1
2
3
4
• y-intercept = 1• slope = 1/2
-4 -3 -2 -1 0 1 2 3 4 5 6
-1
0
1
2
3
4
Scatter Plots
• A scatter plot is a graph of (x,y) points, but without a line connecting all of them. 0 50 100 150 200 250 300 350
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
200.00
Boiling Point
Free
zing
Poi
nt
Scatter Plots
• A best fit line is a line that is close to the points in a scatter plot.
0 50 100 150 200 250 300 350
-150.00
-100.00
-50.00
0.00
50.00
100.00
150.00
200.00
f(x) = 0.731618438 x − 99.16360061
Boiling Point
Free
zing
Poi
nt
Picture from Wikipedia, Author Sandbh
Experiments in Panama
We know that tree seeds are sometimes killed by fungus.
How do seeds defend themselves?
Are there ways to classify how different fungi act?
Photo by Simon Stump
The Experiment
• Took clean seeds, and exposed them to different kinds of fungus.
• Measured if the fungus attacked the seeds.
Photo by Simon Stump
Hypothesis 1
• Specialist fungi will have higher infection rates (positive slope).
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50
0.2
0.4
0.6
0.8
1
Degree of Specialization
% o
f see
ds in
fect
ed
Data from Stump and Arnold, Unpublished
Hypothesis 1
• Specialist fungi will have higher infection rates (positive slope).
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50
0.2
0.4
0.6
0.8
1
Degree of Specialization
% o
f see
ds in
fect
ed
Data from Stump and Arnold, Unpublished
Hypothesis 2• If a fungus has a really high infection rate, then
related fungi should also have a high infection rate. (positive slope)
0.0 0.1 0.2 0.30
0.5
1
1.5
Fungal Relatedness
Dif
fere
nc
e i
n I
nfe
c-
tio
n R
ate
(a)
Data from Stump and Arnold, Unpublished
Hypothesis 2• If a fungus has a really high infection rate, then
related fungi should also have a high infection rate. (positive slope)
0.0 0.1 0.2 0.30
0.5
1
1.5
Fungal Relatedness
Dif
fere
nc
e i
n I
nfe
c-
tio
n R
ate
(a)
Data from Stump and Arnold, Unpublished
Activity
0.75 1.25 1.75 2.250
0.2
0.4
0.6
0.8
1
Fungus Frequency
% o
f se
eds
infe
cted
Data from Stump and Arnold, Unpublished