HP HP-11C - Linear Regression

Section 3: Numeric Functions 63
Linear Regression
Linear regression is a statistical
method for finding a straight line
that best fits a set of two or more data
pairs, thus providing a relationship
between two variables. After the
statistics of a group of data pairs has
been accumulated in register R,
through Rs, you can calculate the
coefficients in the linear equation y =
Ax + B using the least squares
method by pressing [f][L.R.].
To use the linear regression function on your HP-11C, use the
key to accumulate the statistics of a series of two or more data
pairs. Then execute [LR.]. When you press [f][L.R]:
1. The contents of the stack registers are lifted just as they are
when you press [RCL][ X +], as described on page 57.
2. Theslope (A) and the y-intercept (B) of the least squares line
of the data are calculated using the equations:
_ n3xy—3x3y _ Yy3sx?—3x3xy
n3x?—(3x)? n3x?—(3x)?
The slope A is placed
in the Y-register; the T
y-intercept, B, is _ 7%
p}acec(ii )l(n thet dis- Y & [slope(A)
played X-register. X # |y-intercept (B)
Example: Calculate the y-intercept and slope of Voltz’s corrected
data.
Solution: Voltz could draw a plot of coal production against
electrical output, like the one in the following illustration.
However, with her HP-11C, Voltz has only to accumulate the
statistics (as we have already done) using the key, then press
[LR].