Linear regression and allometry

1
Linear regressionand allometry

1. Linear regression different types 2.
Allometry concepts 3. Analysis using
morpho-tools
2
Question 1 you are testing for a linear
relationship between face height and braincase
depth. a. Sketch the plot as you would expect it
to appear. -axes-data etc.
3
Question 1 you are testing for a linear
relationship between face height and braincase
depth. a. Sketch the plot as you would expect it
to appear. b. What is your model for the
relationship between the two variables?
y braincase depth
x face height
4
Question 1 you are testing for a linear
relationship between face height and braincase
depth. a. Sketch the plot as you would expect it
to appear. b. What is your model for the
relationship between the two variables? Y a
bX e, using ____ regression (why?) What are
these things? a, b, e
y braincase depth
x face height
5
Question 2 you are testing for a allometry in
face height a. Sketch the plot as you would
expect it to appear. -axes-data etc.
6
Question 2 you are testing for a allometry in
braincase depth a. Sketch the plot as you would
expect it to appear. Bivariate allometry is
linear regression, with axes Log-scaled, and the
x-axis is a measure of size
y Logbraincase depth
x Logbody size
7
Allometry What do these things mean in terms of
real morphology?
Positive Allometry Slope gt 1.0
Negative Allometry Slope lt 1.0
8
Two dogs, scaled to the same head size
Is there allometry? What structure(s)?
9
What sort of plot would you expect if Y eye
width? (assuming other dogs follow the trend)
size LxW
Y
10
What sort of plot would you expect if Y eye
width? (assuming other dogs follow the trend)
size LxW
Y
11
Practical 3 Linear regression allometry
-3) select relocatable landmarks -2) place
landmarks on all specimens -1) decide on
measurement net, 0) compute measurements across
a measurement net for all specimens 1) select a
size measurement 2) perform a regression analysis
on morpho-tools.net 3) plot the allometry net
12
Size
Skull length e.g., 10-13Mean of all lengths on
the distance netSkull area (can compute in
ImageJ)Centroid size (youll learn how to
compute it next week)
13
Perform the regression analysis
Simply use the output of lab 2 the set of
Euclidean distances for all of your measurements
across all specimens with a size column added
14
morpho-tools...
whats this?
15
morpho-tools...
At a 95 confidence level, the slope for
measurement 1 lies in the range (1.27, 1.55).
This doesnt include 1.0. For meas. 2, the 95
C.I. includes 1.0, so we cant reject isometry.
16
Lab 3 Linear regression
size centroid size, method major axis
17
Lab 3 Linear regression
18
Perform the regression analysis
Now, take those results and put them into column
4 of your measurement net spreadsheet
...and rerun the measurement net pages
19
Lab 3 Linear regression and bivariate allometry
size centroid size
Positive allometryIsometryNegative
allometryNot significant (3-15)
Interpret these patterns as a biologist!
20
and.. oh, lil Chihuahua!... were your head to
shrink,the beauty of your eyes would only grow,
I think,because the blessed touch of Allometry,
I hypothesize,will ensure they (relatively) grow
even as you diminish in size