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Vernier Graphical Analysis 3 Manual de usuario Pagina 23

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Graphical Analysis for Windows TEACHER’S MANUAL
25
General Notes
Statistics
The standard deviation used in statistical calculations is
std.dev.=
−⋅
∑
−
xnx
n
im
22
1
where x
m
= mean
n = number of data points
This is sometimes referred to as the sample standard deviation.
The program calculates the “best fit” line using linear regression by the method of least squares. The equations used are
()
()
()
()
()
slope M==
⋅
∑
⋅−
∑
⋅
∑
⋅
∑
−
∑
n
i
x
i
y
i
x
i
y
nx
i
x
i
2
2
()
()
()
()
()
()
intercept B==
∑
⋅
∑
−
∑
⋅
∑
⋅
∑
−
∑
x
i
y
i
x
i
i
x
y
nx
i
x
i
i
2
2
2
correlation coefficient =
()()
()()
xx yy
xx yy
mm
mm
11
1
2
1
2
−⋅−
−⋅ −
∑
∑∑
()()
correlation coefficient =
⋅
∑
−⋅ ⋅
∑
−⋅ ⋅
∑
−⋅
i
x
i
y
n
m
x
m
y
xn
m
x
yny
iim
222
2
()
()
std. dev. of slope =
n
y
nx
i
x
i
⋅
⋅
∑
−
∑
2
2
2
σ
()
()
std. dev. of y - intercept =
y
x
nx
i
x
i
i
2
2
2
2
σ
⋅
∑
⋅
∑
−
∑
where n = number of data pairs
x
m
= mean of x-values
y
m
= mean of y-values
()
y
n
i
y
BM
i
x
2
1
2
2
σ
=
−
⋅−−⋅
∑
When Graphical Analysis performs automatic or manual curve fits, it calculates and reports the mean square error which
is
()
mean square error
=
−
′
∑
2
i
y
i
y
n
where y
I
= the y-value of each data point
y
I
´ = the y-value of the curve fit
n = number of data points.
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