linear regrssion, exponential regression, and power regression?

Question

what are they and how do you find them with a given data set?

can i do all this on excel or ti calculator?

Answer 1

All three are the fitting of a curve (or line) to a set of data so that the rms error between the curve and all the data points is a minimum.
Linear regression:
y = a + bx
Exponential regression
y = ae^bx
Ln(y) = Ln(a) + bx
Power regression
y = ab^x
Ln(y) = Ln(a) + xLn(b)
For a paired data set (xi,Fi)
the matrix
n. . ∑x. . a ∑F
∑x. ∑x^2 b ∑xF
solves for linear regression,
the matrix
n. . ∑x. . Ln(a) ∑Ln(F)
∑x. ∑x^2. . b. ∑xLn(F)
solves for exponential regression, and
the matrix
n. . ∑x. . Ln(a) ∑Ln(F)
∑x. ∑x^2 Ln(b) ∑xLn(F)
solves for power regression.

Answer 2

The data set for this sort of thing consists of a bunch of pairs of numbers (times paired with temperatures, heights paired with weights, etc.). Imagine treating each pair of numbers in the data set as an ordered pair (x,y), and graphing all of those points; this amounts to making a scatter plot of the data. Linear regression means finding the straight line that "comes closest" (in some precisely defined sense) to all of those points. Similarly, exponential regression means finding the exponential curve that comes closest to all the points, and power regression means finding the polynomial curve that comes closest to all the points.
It's extremely tedious to determine the equations of these lines and/or curves if there are more than a handful of data points, so in practice some kind of technology is almost always used.