Trident Help

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.

NumberTypeUse it for
11-VariableOne list of values (mean, spread, quartiles).
2y=a+bxStraight-line regression.
3y=a+bx+cx²Quadratic regression.
4y=a+b·ln(x)Logarithmic regression.
5y=a·e^(bx)Exponential regression.
6y=a·b^xAnother exponential form.
7y=a·x^bPower regression.
8y=a+b/xReciprocal regression.
Example 12.1

The type menu

  1. MENU 6.

    MENU6
Result of the example "The type menu" The display shows: 1:1-Variable / 2:y=a+bx / 3:y=a+bx+cx² / 4:y=a+b·ln(x).
You should see1:1-Variable 2:y=a+bx

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

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

    MENU611=2=3=4=
Result of the example "Enter four values" The display shows: x / 1 / 2 / 3 / 4 / x5=.
You should seex5=
Example 12.3

Delete a row

  1. Enter 1, 2, then go up and delete the second row.

    MENU611=2=▲DEL
Result of the example "Delete a row" The display shows: x / 1 / x2=.
You should seex2=
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

  1. Enter 1, 2, 3, 4, then OPTN 3.

    MENU611=2=3=4=OPTN3
Result of the example "Mean and sums" The display shows: x̄=2.5 / Σx=10 / Σx²=30 / σ²x=1.25.
You should seex̄=2.5 Σx=10 Σx²=30 σ²x=1.25
Example 12.5

Sample deviation

  1. Scroll down six lines.

    MENU611=2=3=4=OPTN3▼▼▼▼▼▼
Result of the example "Sample deviation" The display shows: sx=1.290994449 / n=4 / min(x)=1 / Q1=1.5.
You should seesx=1.290994449 n=4
Example 12.6

Quartiles and median

  1. Scroll to the end of the list.

    MENU611=2=3=4=OPTN3▼▼▼▼▼▼▼▼▼
Result of the example "Quartiles and median" The display shows: Q1=1.5 / Med=2.5 / Q3=3.5 / max(x)=4.
You should seeQ1=1.5 Med=2.5 Q3=3.5 max(x)=4
xˉ=∑xn,σx=∑(x−xˉ)2n,sx=∑(x−xˉ)2n−1\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

  1. Frequency On, then 1-Variable.

    SHIFTSETUPMENU61MENU61
  2. Enter 1, 2, 3, then go to the top of the Freq column.

    1=2=3=▲▲▲▶
  3. Freq 4 for x = 1, then 1 for x = 2. Calculate.

    4=1=OPTN3
Result of the example "Weighted mean" The display shows: x̄=1.5 / Σx=9 / Σx²=17 / σ²x=0.5833333333.
You should seex̄=1.5 Σx=9

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

  1. Choose y=a+bx and type x = 1, 2, 3.

    MENU621=2=3=
  2. Go to the top of the y column and type 2, 4, 6. Calculate.

    ▶▲▲▲2=4=6=OPTN3
Result of the example "A perfect line" The display shows: y=a+bx / a=0 / b=2 / r=1.
You should seea=0 b=2 r=1
Example 12.9

A rough line

  1. x = 1, 2, 3 and y = 2, 4, 7.

    MENU621=2=3=▶▲▲▲2=4=7=OPTN3
Result of the example "A rough line" The display shows: y=a+bx / a=-0.6666666667 / b=2.5 / r=0.9933992678.
You should seeb=2.5 r=0.9933992678
y=a+bx,b=SxySxx,a=yˉ−bxˉy=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

  1. Type 3 (quadratic). x = 1, 2, 3 and y = 2, 4, 7.

    MENU631=2=3=▶▲▲▲2=4=7=OPTN3
Result of the example "Quadratic through three points" The display shows: y=a+bx+cx² / a=1 / b=0.5 / c=0.5.
You should seea=1 b=0.5 c=0.5
Example 12.11

Exponential y = a·b^x

  1. Type 6. x = 0, 1, 2 and y = 3, 6, 12.

    MENU660=1=2=▶▲▲▲3=6=12=OPTN3
Result of the example "Exponential y = a·b^x" The display shows: y=a·b^x / a=3 / b=2 / r=1.
You should seea=3 b=2

12.7The statistics OPTN menu#

OPTN numberItemWhat it does
1Select TypeChoose a different statistics type.
2EditorGo to the data editor.
31-Variable Calc / Regression CalcShow the results for the current type.
4Delete AllErase all the data and start a fresh editor.
Example 12.12

The OPTN list in Statistics

  1. Enter a value and press OPTN.

    MENU611=OPTN
Result of the example "The OPTN list in Statistics" The display shows: 1:Select Type / 2:Editor / 3:1-Variable Calc / 4:Delete All.
You should see1:Select Type 2:Editor 3:1-Variable Calc 4:Delete All
Example 12.13

Delete All data

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

    MENU611=2=OPTN4OPTN2
Result of the example "Delete All data" The display shows: x / x1=.
You should seex1=

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