RPN Scientific 15 manual · Chapter 8 of 12

Statistics and regression

Enter one-variable and two-variable data with Σ+, then find the mean, standard deviation, linear regression line, estimates and correlation.

8.1Enter data with Σ+#

Statistics collect data into the registers R2 to R7: R2 holds the count n, R3 the sum of x, R4 the sum of x², R5 the sum of y, R6 the sum of y² and R7 the sum of xy.

To add a data point with two variables, put y in Y and x in X (key in y, ENTER, x) and press Σ+ (Σ+). The display shows n, the number of points so far. For one variable, simply key in x and press Σ+.

Example 8.1

Enter three data points

Clear old data with f Σ. Enter (x, y) = (3, 2), (5, 4) and (8, 6). Each is y, ENTER, x, Σ+.
fCLR ΣGSB2ENTER3Σ+4ENTER5Σ+6ENTER8Σ+

y
ENTER
x
Σ+
n is shown

Entering one data point.

Register	Holds
R2	$n$ , the number of points
R3	$\sum x$
R4	$\sum x^{2}$
R5	$\sum y$
R6	$\sum y^{2}$
R7	$\sum xy$

8.2Find the mean and standard deviation#

\bar{x}=\frac{\sum x}{n}\qquad s_x=\sqrt{\frac{n\sum x^{2}-\left(\sum x\right)^{2}}{n(n-1)}}

The mean and the sample standard deviation (the same for y).

gx̄0 (x̄) gives the mean of x in X and the mean of y in Y. gs. (s) gives the sample standard deviation: s of x in X and s of y in Y. Both need at least two data points (the mean needs one).

Example 8.2

Mean of x and y

Enter the data from before, then press g, x̄.
fCLR ΣGSB2ENTER3Σ+4ENTER5Σ+6ENTER8Σ+gx̄0

Example 8.3

Standard deviation

Enter the data, then press g, s.
fCLR ΣGSB2ENTER3Σ+4ENTER5Σ+6ENTER8Σ+gs.

Example 8.4

Mean of one variable

Clear, then enter 5, 7 and 9 with Σ+ and press g, x̄.
fCLR ΣGSB5Σ+7Σ+9Σ+gx̄0

8.3Fit a straight line: linear regression#

y=A+Bx\qquad B=\frac{n\sum xy-\sum x\sum y}{n\sum x^{2}-\left(\sum x\right)^{2}}\qquad A=\bar{y}-B\bar{x}

The least-squares line that L.R. fits.

fL.R.Σ+ (L.R.) fits the line y = A + Bx to your data. The intercept A comes back in X and the slope B in Y.

Example 8.5

Slope and intercept

Enter the data (3, 2), (5, 4), (8, 6) and press f, L.R.
fCLR ΣGSB2ENTER3Σ+4ENTER5Σ+6ENTER8Σ+fL.R.Σ+

8.4Estimate y and find the correlation#

r=\frac{n\sum xy-\sum x\sum y}{\sqrt{\left(n\sum x^{2}-(\sum x)^{2}\right)\left(n\sum y^{2}-(\sum y)^{2}\right)}}

The correlation coefficient r.

Key in an x value and press fŷ,r. (ŷ,r). X shows the y value predicted by the fitted line. Y shows the correlation coefficient r, which is between −1 and 1. A value near 1 or −1 means the points lie close to a line.

Example 8.6

Estimate y when x is 5

Enter the data. Key in 5 and press f, ŷ,r.
fCLR ΣGSB2ENTER3Σ+4ENTER5Σ+6ENTER8Σ+5fŷ,r.

8.5Remove or correct a data point#

To remove a point you entered by mistake, key in exactly the same y and x, and press gΣ−Σ+ (Σ−). The count n goes down by one. To fix a point, remove the wrong one and then enter the right one.

Example 8.7

Remove a point

Enter three points, then remove the last one by keying it in again with Σ−.
fCLR ΣGSB2ENTER3Σ+4ENTER5Σ+6ENTER8Σ+6ENTER8gΣ−Σ+

8.6Read the sums and the count#

Recall any statistics register with RCL: RCL 2 gives n, RCL 3 gives Σx, and so on. RCL then Σ+ puts Σx in X and Σy in Y in one go. You can also store into these registers, but that changes the statistics.

Example 8.8

Sums of x and y

Enter the three points, then press RCL, Σ+.
fCLR ΣGSB2ENTER3Σ+4ENTER5Σ+6ENTER8Σ+RCLΣ+

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