HP -11C Owner's Handbook Manual page 33

62 Section 3: Numeric Functions
3. The standard deviation of the y values (s,) is calculated
using the statistical data accumulated in registers R,(Xy"),
R,(Zy), and Ro(n) according to the formula shown above.
The resultant value for s, is available in the Y-register.
Example. Calculate the standard deviation for the corrected coal
production and electrical output accumulations used in the
previous examples.
Keystrokes
(is)
Display
0.4287 Standard deviation of
electrical output (X-
register inputs) for the
five-year period.
Standard deviation of coal
production (Y-register
inputs) for the five-year
period.
x2y 0.0800
Retain the preceding statistics in your HP-11C for use in the next
example.
When your data constitutes not just a sample of a population but
rather all of the population, the standard deviation of the data is
the true population standard deviation (denoted o). The formula for
the true population standard deviation differs by a factor of
[(n — 1)/n]* from the formula used for the [5] function. The
difference between the values is small, and for most applications
can be ignored. Nevertheless, if you want to calculate the exact
value of the population standard deviation for an entire
population, you can easily do so with just a few keystrokes on your
HP-11C. Simply add, using the [Z+])key, the mean (£) of the data to
the data and then press [@] [s]. The result will be the true
population standard deviation of the original data.
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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 r
pairs, thus providing a relationship
between two variables. After the
statistics of a group of data pairs has
been accumulated in register Rp
through R;, you can calculate the
coefficients in the linear equation y =
Ax + B using the least squares
method by pressing [f)[CR).
a
To use the linear regression function on your HP-11C, use the (2+
key to accumulate the statistics of a series of two or more data
pairs. Then execute (CR.]. When you press [f) :
1. The contents of the stack registers are lifted just as they are
when you press [RCL][_£+], 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:
_ nixy—Exty B- Yyix2—Vxdxy
n3x?— (x)? nXx?— (Xx)?
The slope A is placed
in the Y-register; the ™T>
y-intercept, B, is ff LR] = zZ>
placed in the dis-
played X-register.
Y>
x»>
Example: Calculate the y-intercept and slope of Voltz's corrected
data.
Solution: Voltz cou/d 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 [2+] key, then press
Ola).