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Statistical Calculations (STAT)

To start a statistical calculation, perform the key operation (STAT) to enter the STAT Mode and then use the screen that appears to select the type of calculation you want to perform.

To select this type of statistical calculation:

(Regression formula shown in parentheses)

 Press this key:
Single-variable (X) (1-VAR)
Paired-variable (X, Y), linear regression

(y = A + Bx)

 (A+BX)
Paired-variable (X, Y), quadratic regression

(y = A + Bx + Cx2)

 (_+CX2)
Paired-variable (X, Y), logarithmic regression

(y = A + Blnx)

 (ln X)
Paired-variable (X, Y), e exponential regression

(y = A eBx)

 (e∧X)
Paired-variable (X, Y), ab exponential regression

(y = ABx)

 (A•B∧X)
Paired-variable (X, Y), power regression

(y = AxB)

 (A•X∧B)
Paired-variable (X, Y), inverse regression

(y = A + B/x)

 (1/X)

Pressing any of the above keys ( to ) displays the Statistics Editor.


Note

When you want to change the calculation type after entering the STAT Mode, perform the key operation (STAT)(Type) to display the calculation type selection screen.

Inputting Data

Use the Statistics Editor to input data. Perform the following key operation to display the Statistics Editor: (STAT)(Data).
The Statistics Editor provides 80 rows for data input when there is an X column only, 40 rows when there are X and FREQ columns or X and Y columns, or 26 rows when there are X, Y, and FREQ columns.


Note

Use the FREQ (frequency) column to input the quantity (frequency) of identical data items. Display of the FREQ column can be turned on (displayed) or off (not displayed) using the Stat Format setting on the setup menu.

Example 1: To select linear regression and input the following data: (170, 66), (173, 68), (179, 75)

  • (STAT)(A+BX)
  • 170173179
  • 666875

Important!

All data currently input in the Statistics Editor is deleted whenever you exit the STAT Mode, switch between the single-variable and a paired-variable statistical calculation type, or change the Stat Format setting on the setup menu.

The following operations are not supported by the Statistics Editor: , (M-), (STO). Pol, Rec, and multi-statements also cannot be input with the Statistics Editor.


To change the data in a cell:

In the Statistics Editor, move the cursor to the cell that contains the data you want to change, input the new data, and then press .

To delete a line:

In the Statistics Editor, move the cursor to the line that you want to delete and then press .

To insert a line:

In the Statistics Editor, move the cursor to the location where you want to insert the line and then perform the following key operation:
(STAT)(Edit)(Ins).

To delete all Statistics Editor contents:

In the Statistics Editor, perform the following key operation:
(STAT)(Edit)(Del-A).


Statistics Calculation Screen

The Statistics Calculation Screen is for performing statistical calculations with the data you input with the Statistics Editor. Pressing the key while the Statistics Editor is displayed switches to the Statistics Calculation Screen.


Using the Statistics Menu

While the Statistics Calculation Screen is on the display, press (STAT) to display the Statistics Menu.
The content to the Statistics Menu depends on whether the currently selected statistical operation type uses a single variable or paired variables.

  • Single-variable Statistics

  • Paired-variables Statistics


Statistics Menu Items

Common Items

Select this menu item: When you want to obtain this:
(Type) Display the calculation type selection screen
(Data) Display the Statistics Editor
(Sum) Display the Sum sub-menu of commands for calculating sums
(Var) Display the Var sub-menu of commands for calculating the mean, standard deviation, etc.
Single-variable: (Distr) Display the Distr sub-menu of commands for normal distribution calculations
• For more information, see "Performing Normal Distribution Calculations".
Paired-variable: (Reg) Display the Reg sub-menu of commands for regression calculations
• For details see "Commands when Linear Regression Calculation (A+BX) Is Selected" and "Commands when Quadratic Regression Calculation (_+CX2) Is Selected".
(MinMax) Display the MinMax sub-menu of commands for obtaining maximum and minimum values

Single-variable (1-VAR) Statistical Calculation Commands

Sum Sub-menu ((STAT)(Sum))

Select this menu item: When you want to obtain this:
(∑x2) Sum of squares of the sample data
(∑x) Sum of the sample data

Var Sub-menu ((STAT)(Var))

Select this menu item: When you want to obtain this:
(n) Number of samples
(x) Mean of the sample data
(σx) Population standard deviation
(sx) Sample standard deviation

Distr Sub-menu ((STAT)(Distr))

(P() This menu can be used to calculate the probability of standard normal distribution.
• For details see "Performing Normal Distribution Calculations".
(Q()
(R()
(t)

MinMax Sub-menu ((STAT)(MinMax))

Select this menu item: When you want to obtain this:
(minX) Minimum value
(maxX) Maximum value

Commands when Linear Regression Calculation (A+BX) Is Selected

Sum Sub-menu ((STAT)(Sum))

Select this menu item: When you want to obtain this:
(∑x2) Sum of squares of the X-data
(∑x) Sum of the X-data
(∑y2) Sum of squares of the Y-data
(∑y) Sum of the Y-data
(∑xy) Sum of products of the X-data and Y-data
(∑x3) Sum of cubes of the X-data
(∑x2y) Sum of (X-data squares × Y-data)
(∑x4) Sum of biquadrate of the X-data

Var Sub-menu ((STAT)(Var))

Select this menu item: When you want to obtain this:
(n) Number of samples
(x) Mean of the X-data
(σx) Population standard deviation of the X-data
(sx) Sample standard deviation of the X-data
(y) Mean of the Y-data
(σy) Population standard deviation of the Y-data
(sy) Sample standard deviation of the Y-data

Reg Sub-menu ((STAT)(Reg))

Select this menu item: When you want to obtain this:
(A) Regression coefficient constant term A
(B) Regression coefficient B
(r) Correlation coefficient r
(xˆ) Estimated value of X
(yˆ) Estimated value of Y

MinMax Sub-menu ((STAT)(MinMax))

Select this menu item: When you want to obtain this:
(minX) Minimum value of the X-data
(maxX) Maximum value of the X-data
(minY) Minimum value of the Y-data
(maxY) Maximum value of the Y-data

Commands when Quadratic Regression Calculation (_+CX2) Is Selected

Reg Sub-menu ((STAT)(Reg))

Select this menu item: When you want to obtain this:
(A) Regression coefficient constant term A
(B) Linear coefficient B of the regression coefficients
(C) Quadratic coefficient C of the regression coefficients
(xˆ1) Estimated value of x1
(xˆ2) Estimated value of x2
(yˆ) Estimated value of y

Note

xˆ, xˆ1, xˆ2 and yˆ are not variables. They are commands of the type that take an argument immediately before them. See "Calculating Estimated Values" for more information.


Example 2: To input the single-variable data x = {1, 2, 2, 3, 3, 3, 4, 4, 5}, using the FREQ column to specify the number of repeats for each items ({xn; freqn} = {1;1, 2;2, 3;3, 4;2, 5;1}), and calculate the mean and population standard deviation.

  • (SETUP)(STAT)(ON)
    (STAT)(1-VAR)
    12345
    1232
  • (STAT)(Var)(x)
  • 3
  • (STAT)(Var)(σx)
  • 1.154700538

Results: Mean: 3, Population Standard Deviation: 1.154700538


Example 3: To calculate the linear regression and logarithmic regression correlation coefficients for the following paired-variable data and determine the regression formula for the strongest correlation: (x, y) = (20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix 3 (three decimal places) for results.

  • (SETUP)(STAT)(OFF)
    (SETUP)(Fix)
    (STAT)(A+BX)
    20110200290
    3150731088009310
  • (STAT)(Reg)(r)
  • 0.923
  • (STAT)(Type)(ln X)
    (STAT)(Reg)(r)
  • 0.998
  • (STAT)(Reg)(A)
  • -3857.984
  • (STAT)(Reg)(B)
  • 2357.532

Results: Linear Regression Correlation Coefficient: 0.923
Logarithmic Regression Correlation Coefficient: 0.998
Logarithmic Regression Formula: y = -3857.984 + 2357.532lnx


Calculating Estimated Values

Based on the regression formula obtained by paired-variable statistical calculation, the estimated value of y can be calculated for a given x-value.
The corresponding x-value (two values, x1 and x2, in the case of quadratic regression) also can be calculated for a value of y in the regression formula.


Example 4: To determine the estimate value for x when y = -130 in the regression formula produced by logarithmic regression of the data in Example 3. Specify Fix 3 for the result. (Perform the following operation after completing the operations in Example 3.)

  • 130(STAT)(Reg)(xˆ)
  • 4.861

Important!

Regression coefficient, correlation coefficient, and estimated value calculations can take considerable time when there are a large number of data items.


Performing Normal Distribution Calculations

While single-variable statistical calculation is selected, you can perform normal distribution calculation using the functions shown below from the menu that appears when you perform the following key operation: (STAT)(Distr).

P, Q, R: These functions take the argument t and determine a probability of standard normal distribution as illustrated below.

t: This function is preceded by the argument X, and determines the normalized variate Xt = X - xσx.


Example 5: For the single variable data {xn; freqn} = {0;1, 1;2, 2;1, 3;2, 4;2, 5;2, 6;3, 7;4, 9;2, 10;1}, to determine the normalized variate (t) when x = 3, and P(t) at that point up to three decimal places (Fix 3).

  • (SETUP)(STAT)(ON)
    (SETUP)(Fix)
    (STAT)(1-VAR)
  • 01234567910

    1212223421
  • 3(STAT)(Distr)(t)
  • (STAT)(Distr)(P()

Results: Normalized variate (t): -0.762
P(t): 0.223

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