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Introducing the Topic
In this chapter, you and your students will learn how to use the Sharp graphing
calculator to find several regression equations for a set of data points and then
determine the model of "best fit." A regression equation is a model of the
relationship between the dependent variable Y and the independent variable X.
Other regression models include y = ax
2
+ bx + c (quadratic), y = ax
3
+ bx
2
+ cx +
d (cubic), y = ax
4
+ bx
3
+ cx
2
+ dx + e (quartic), y = a + b ln x (natural logarithm),
y = a + b log x (common logarithm), y = a*bx (exponential), y = a*ebX (natural
exponential), y = a + bx
-1
(inverse), and Y = a*Xb (power). The a, b, c, d and e are
calculated for each model in order to find the best-fitting curve (minimized error).
A third value, r
2
, is calculated for each regression and is a measure of how well
the equation fits the data points, and it will range from 0 to 1. If r
2
= 1, then the
equation intersects all the data points, and the model is said to have perfect fit.
Values of r
2
close to 1 are said to reflect a good fit, and values close to 0 are said
to reflect a poor fit.
44 Other Regressions and Model of “Best Fit”/STATISTICS USING THE SHARP EL-9600
OTHER REGRESSIONS
AND MODEL OF “BEST FIT”
Chapter nine