### Standard Error

How is the standard error calculated?
SE=âˆš
[(Î£C^{2} -
bÎ£C - mÎ£SC)/(n-2)]
where S = log of
scale or
size, C = log of
count, n =
number of sizes,
b = y-intercept of the regression line,
m = slope of the
regression lineÂ Â

### Regression Line

How is the slope of the regression line calculated?
The slope of the
regression line, m,
used for calculating the
D_{B} =
m =
(nÎ£SC - Î£SÎ£C)/(nÎ£S^{2}
- (Î£S)^{2})
Â where S = log of scale
or size, C = log of
count, n =
number of sizes,
m = slope of the regression line

For other regression lines, S=the value along the x-axis, and y = the value along the y-axis.Â Â

### Correlation

How is the correlation (r^{2})
for the regression line calculated?
r^{2}= **[**(nÎ£SC-Î£SÎ£C)/âˆš
[(nÎ£S^{2}-(Î£S)^{2})(nÎ£C^{2}-(Î£C)^{2})]
**] ^{2}**
where S = log of scale or
size, C = log of
count, n =
number of
sizes, b =
y-intercept of the regression line

### Y-intercept

How is the y-intercept of the regression line calculated? y int = (Î£C-mÎ£S)/n where S = log of scale or size, C = log of count, n = number of sizes, m = slope of the regression line

### Prefactor

How is the prefactor for the scaling rule
calculated?
The prefactor A:
A = Euler’s *e*^{y-int}
y = AX^{DB}
Where for y = AX^{DB}, -D_{B}
=
slope of the regression line and y-int =
the y-intercept of the regression lineÂ

### CV

CV stands for coefficient of variation = standard deviation/mean.
CV^{2} =
[Ïƒ/Î¼]^{2}=Î›
In FracLac, it is used to calculate
lacunarity It
is a measure of variation in pixel distribution for
regular box counting
and sliding box lacunarity.
It measures variation in a set of data and is calculated
as the standard
deviation over the mean for the data. It can be
multiplied by 100 or squared, depending on
the usage.