MathU™ RPN 2.2 for iPhone
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Statistics Functions

The statistical functions accumulate sums based on the values in the x and y stack registers. These sums are used to compute the mean and standard deviation σ or can be accessed directly via RCL. Use CL Σ to reset all the statistical registers to zero before accumulating sums. If you make a mistake keying in the x,y values and after pressing Σ+, re-key the errant values and press Σ− to remove them from the sums. The mean and standard deviation are computed as

with similar equations holding for the y component as well.

Key	Function	Description	Effect on stack
Σ+	stats+	Accumulate x,y	n is the number of sums accumulated so far.
Σ−	stats-	Remove x,y	n is the number of sums accumulated so far.
RCL Σ+	rcl	Recall statistics sums.
	mean	Mean
σ	std	Standard deviation
CL Σ	clstats	Clear statistical registers
N!	fact	Factorial
RAND	rand	Random number from 0 to 1.0 (uniformly distributed) or random integer (when in a non-decimal number base)
%	%	Percent
%T	%T	Percent of total
%CH	% ch	Percent change
y,r	ye	Linear estimate of y and correlation coefficient
x,r	xe	Linear estimate of x and correlation coefficient

The statistical sums are strored in these registers:

RCL . n to access the sums in the secondary registers.

Linear Regression

MathU RPN includes two functions to fit linear trend lines to a set of data, y,r and x,r. The first uses the linear trend to estimate x given a value of y, the second uses the linear trend to estimate y given a value of x. Both functions rely on the statistics registers to hold information about the data points.

The functions also return a goodness of fit parameter, called the correlation coefficient r. r will be near 1.0 or -1.0 for data that is accurately described by the linear fit and values near zero for data that does not have a clear linear trend.

The figures below show two situations, one with a linear trend and another that is not very well estimated by a linear trend. The correlation coefficient for each situation is shown.

To perform a linear regression:

1. CLΣ to clear the statistics registers

2. Enter the data points via y ENTER x Σ+

3. Repeat step 2 for each point in the data set.
4. To estimate a y value given an x, enter the x value followed by y,r
5. To estimate an x value given a y value, enter the x value followed by x,r

Determining the trend line parameters

You can use the y,r and x,r functions to determine the equation of the trend line, y = m*x + b:

1. Enter the data points into the statistics registers as described above.
2. 0 y,r to determine b by computing the estimated y when x is 0.0
3. STO 0 to store b in register 0 (in order to remember it)
4. 1 y,r to estimate value of y when x is 1.0
5. RCL 0 − to compute the slope m.

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