Natural Scientific 991 manual · Chapter 12 of 18

Statistics and regression

Enter data in the editor, then get one-variable statistics, regression lines and curves.

12.1Open Statistics and pick a type#

Press MENU then 6. A menu asks for the type of data.

Number	Type	Use it for
1	1-Variable	One list of values (mean, spread, quartiles).
2	y=a+bx	Straight-line regression.
3	y=a+bx+cx²	Quadratic regression.
4	y=a+b·ln(x)	Logarithmic regression.
5	y=a·e^(bx)	Exponential regression.
6	y=a·b^x	Another exponential form.
7	y=a·x^b	Power regression.
8	y=a+b/x	Reciprocal regression.

Example 12.1

The type menu

MENU 6.
MENU6

12.2Enter and edit data#

The editor is a table with an x column (and y for two-variable types). Type a number and press = to store it and move to the next row. Use ▲, ▼, ◀ and ▶ to move around, type over a value to change it, and DEL to delete the row. Press AC to leave the editor; OPTN brings up the statistics menu from the editor.

Example 12.2

Enter four values

Open Statistics, choose 1-Variable, and type 1, 2, 3, 4.
MENU611=2=3=4=

Example 12.3

Delete a row

Enter 1, 2, then go up and delete the second row.
MENU611=2=▲DEL

The two-variable editor The display shows: x | y / 1 | 0 / 2 | 0 / | / x3=. — The two-variable editor

12.3Find the mean and standard deviation#

Press OPTN then 3 (1-Variable Calc). The results list shows: x̄, Σx, Σx², σ²x, σx, s²x, sx, n, min(x), Q1, Med, Q3, max(x). Scroll with ▼. σ is the population standard deviation and s is the sample standard deviation. Press AC to go back to the editor.

Example 12.4

Mean and sums

Enter 1, 2, 3, 4, then OPTN 3.
MENU611=2=3=4=OPTN3

Example 12.5

Sample deviation

Scroll down six lines.
MENU611=2=3=4=OPTN3▼▼▼▼▼▼

Example 12.6

Quartiles and median

Scroll to the end of the list.
MENU611=2=3=4=OPTN3▼▼▼▼▼▼▼▼▼

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

Mean, population and sample standard deviation

12.4Use a frequency column#

Turn on Frequency in SETUP (SETUP, 6, 1) before choosing the type. The editor gets a Freq column. Enter your values first, then go back up and right to fill in how many times each value occurs. A blank Freq counts as 1.

Example 12.7

Weighted mean

Frequency On, then 1-Variable.
SHIFTSETUPMENU61MENU61
Enter 1, 2, 3, then go to the top of the Freq column.
1=2=3=▲▲▲▶
Freq 4 for x = 1, then 1 for x = 2. Calculate.
4=1=OPTN3

12.5Fit a straight line (linear regression)#

Choose type 2 (y=a+bx). Enter all the x values, then go up and right to the y column and enter the y values, then press OPTN and 3 (Regression Calc). The results show a, b and the correlation coefficient r.

Example 12.8

A perfect line

Choose y=a+bx and type x = 1, 2, 3.
MENU621=2=3=
Go to the top of the y column and type 2, 4, 6. Calculate.
▶▲▲▲2=4=6=OPTN3

Example 12.9

A rough line

x = 1, 2, 3 and y = 2, 4, 7.
MENU621=2=3=▶▲▲▲2=4=7=OPTN3

y=a+bx,\qquad b=\frac{S_{xy}}{S_{xx}},\quad a=\bar y-b\bar x

Least-squares line

12.6Quadratic, exponential and other fits#

Types 3 to 8 work the same way. The results give a, b and (for the quadratic) c, with r for the others. For y=a+b/x, the x values cannot be zero. The a·e^(bx) type reports b as the exponent; the a·b^x type reports b as the base.

Example 12.10

Quadratic through three points

Type 3 (quadratic). x = 1, 2, 3 and y = 2, 4, 7.
MENU631=2=3=▶▲▲▲2=4=7=OPTN3

Example 12.11

Exponential y = a·b^x

Type 6. x = 0, 1, 2 and y = 3, 6, 12.
MENU660=1=2=▶▲▲▲3=6=12=OPTN3

12.7The statistics OPTN menu#

OPTN number	Item	What it does
1	Select Type	Choose a different statistics type.
2	Editor	Go to the data editor.
3	1-Variable Calc / Regression Calc	Show the results for the current type.
4	Delete All	Erase all the data and start a fresh editor.

Example 12.12

The OPTN list in Statistics

Enter a value and press OPTN.
MENU611=OPTN

Example 12.13

Delete All data

Enter 1, 2, then OPTN 4 (Delete All), then OPTN 2 to reopen the editor.
MENU611=2=OPTN4OPTN2

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