Casio FXCP400 line, Med-Med, y = a￿x3, + b￿x + c, + c￿x + d, + d￿x + e, Power regression, Regression types:, kRegression graphs, Sinusoidal regression

kRegression 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	Quadratic regression graph	Logistic regression graph
Regression types:
￿ Linear regression (LinearR) [Linear Reg] ..............................................................		y = a￿x + b, y = a + b￿x
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 y-intercept. The graphic representation of this relationship is a linear regression graph.

￿ Med-Med line (MedMed) [MedMed Line] ................................................................................... y = a￿x + b

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]	............................................................. y	= a￿x2	+ b￿x + c
￿ Cubic regression (CubicR) [Cubic Reg]................................................................	y = a￿x3	+ b￿x2	+ c￿x + d
￿ Quartic regression (QuartR) [Quartic Reg].................................................	y = a￿x4 + b￿x3 + c￿x2		+ d￿x + e

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]....................................................................	a + b￿ln(x)
Logarithmic regression expresses y as a logarithmic function of x. The normal logarithmic regression

formula is y = a + b￿ln(x). If we say that X = ln(x), then this formula corresponds to the linear regression formula y = a + b￿X.

￿ a￿ebx Exponential regression (ExpR) [Exponential Reg]............................................................. y = a￿eb￿x

Exponential regression can be used when y is proportional to the exponential function of x. The normal exponential regression formula is y = a￿eb￿x. If we obtain the logarithms of both sides, we get ln(y) = ln(a) + b￿x. Next, if we say that Y = ln(y) and A = In(a), the formula corresponds to the linear regression formula Y = A + b￿x.

￿ a￿bx Exponential regression (abExpR) [abExponential Reg] ........................................................y = a￿bx

Exponential regression can be used when y is proportional to the exponential function of x. The normal exponential regression formula in this case is y = a￿bx. If we take the natural logarithms of both sides, we get ln(y) = ln(a) + (ln(b))￿x. Next, if we say that Y = ln(y), A = ln(a) and B = ln(b), the formula corresponds to the linear regression formula Y = A + B￿x.

￿ Power regression (PowerR) [Power Reg]......................................................................................y = a￿xb

Power regression can be used when y is proportional to the power of x. The normal power regression formula is y = a￿xb. If we obtain the logarithms of both sides, we get ln(y) = ln(a) + b￿ln(x). Next, if we say that X = ln(x), Y = ln(y), and A = ln(a), the formula corresponds to the linear regression formula Y = A + b￿X.

￿ Sinusoidal regression (SinR) [Sinusoidal Reg] ........................................................ y = a￿sin(b￿x + c) + d

Sinusoidal regression is best for data that repeats at a regular fixed interval over time.

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