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

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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

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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.

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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Data from Stump and Arnold, Unpublished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Data from Stump and Arnold, Unpublished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

Diff

eren

ce in

Infe

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Data from Stump and Arnold, Unpublished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

Diff

eren

ce in

Infe

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Data from Stump and Arnold, Unpublished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 see

ds in

fect

ed

Data from Stump and Arnold, Unpublished