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k Regression graphs
Regression graphs of each of the paired-variable data can be drawn according to the model formulas under
"Regression types" below.
Linear regression graph
Regression types:
Linear regression (LinearR) [Linear Reg] ..............................................................
Linear regression uses the method of least squares to determine the equation that best fits your data
points, and returns values for the slope and
linear regression graph.
Med-Med line (MedMed) [MedMed Line] ...................................................................................
When you suspect that the data contains extreme values, you should use the Med-Med graph (which
is based on medians) in place of the linear regression graph. Med-Med graph is similar to the linear
regression graph, but it also minimizes the effects of extreme values.
Quadratic regression (QuadR) [Quadratic Reg] .............................................................
Cubic regression (CubicR) [Cubic Reg] ................................................................
Quartic regression (QuartR) [Quartic Reg] .................................................
Quadratic, cubic, and quartic regression graphs use the method of least squares to draw a curve that
passes the vicinity of as many data points as possible. These graphs can be expressed as quadratic, cubic,
and quartic regression expressions.
Logarithmic regression (LogR) [Logarithmic Reg] ....................................................................
Logarithmic regression expresses
y
a
b
formula is
=
+
y
a
b
formula
=
+
X.
a e
b x
Exponential regression (ExpR) [Exponential Reg].............................................................
Exponential regression can be used when
exponential regression formula is
a
b x
= ln(
) +
. Next, if we say that Y = ln(
b x
formula Y = A +
a b
x
Exponential regression (abExpR) [abExponential Reg] ........................................................
Exponential regression can be used when
exponential regression formula in this case is
y
a
get ln(
) = ln(
) + (ln(
the linear regression formula Y = A + B
Power regression (PowerR) [Power Reg] ......................................................................................
Power regression can be used when y is proportional to the power of
y
a x
b
formula is
=
. If we obtain the logarithms of both sides, we get ln(
x
that X = ln(
), Y = ln(
Sinusoidal regression (SinR) [Sinusoidal Reg] ........................................................
Sinusoidal regression is best for data that repeats at a regular fixed interval over time.
Quadratic regression graph
y
as a logarithmic function of
x
ln(
). If we say that X = ln(
y
a e
b x
=
y
) and A = In(
.
b
x
))
. Next, if we say that Y = ln(
x
.
y
a
), and A = ln(
), the formula corresponds to the linear regression formula Y = A +
y
-intercept. The graphic representation of this relationship is a
x
. The normal logarithmic regression
x
), then this formula corresponds to the linear regression
y
is proportional to the exponential function of
. If we obtain the natural logarithms of both sides, we get ln(
a
), the formula corresponds to the linear regression
y
is proportional to the exponential function of
y
a b
x
=
. If we take the natural logarithms of both sides, we
y
a
), A = ln(
) and B = ln(
Logistic regression graph
y
a x
=
+
y
=
y
a x
3
=
+
y
a x
b x
4
3
=
+
+
x
x
b
), the formula corresponds to
x
. The normal power regression
y
a
b
x
) = ln(
) +
ln(
). Next, if we say
y
a
=
sin(
Chapter 7: Statistics Application 138
b
y
a
b x
,
=
+
y
a x
b
=
+
a x
b x
c
2
+
+
b x
c x
d
2
+
+
c x
d x
e
2
+
+
a
b
x
+
ln(
)
y
a e
b x
=
. The normal
y
)
y
a b
x
=
. The normal
y
a x
b
=
b
X.
b x
c
d
+
) +
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