Statistical Calculations
Statistical Modes
DreamCalc maintains two independent data lists for use in statistical calculations and data plots, namely an X-Y list and a Standard Data (SD) list. The X-Y list is used in regression analysis, and the SD list holds values with weighted frequencies. The calculator's statistical mode designates which list is in current use. You can switch statistical mode instantly from either the Modes->Statistics menu on the main calculator interface or by using the [MODE] key on the Keypad.
The X-Y modes are sub-divided into regression styles, as follows:
| Regression Mode (X-Y) |
Formula |
Transform Model |
| Linear |
y = Ax + B |
|
| Logarithmic |
y = A.ln(x) + B, for x > 0 |
ln(x) & y |
| Exponential |
y = A.eBx, for y > 0 |
x & ln(y) |
| Power |
y = AxB, for x & y > 0 |
ln(x) & ln(y) |
| Inverse |
y = A / x + B, for x not 0 |
1/x & y |
| Quadratic Regression |
y = Ax2 + Bx + C |
|
| Cubic Regression |
y = Ax3 + Bx2 + Cx + D |
|
| Logistic Regression (Pro Only) |
y = A / (1 + B.eCx) |
|
Transform Models
Several regression modes utilize a transform model during calculations, according to the table above. For example, when calculating SUM#X in the logarithmic X-Y mode, the result given will be the sum of ln(x), rather than simply the x-values added together. For modes which don't employ a transform model, i.e. polynomial and logistic regressions, the linear sum would simply be returned.
Keying in Data
List Window
The most convenient method of data input is to use the spreadsheet style interface provided in the Graphing & List Window. The main calculator interface is instantly aware of any modifications you make here.
To display the list window, press F12 at any time.
From the Keypad
If you only have a few data points, or simply want some punishment, you can use the main keypad to add values to the list in sequence.
To enter a value, simply key it in and press [DAT]. You should use the separator key [;] to enter paired values, for example:
45 [;] 3
[DAT]
In Standard Data (SD) mode, this will enter a value of 45 with a frequency of 3, or an X-Y pair in a regression mode. If you omit the frequency in SD mode, a value of 1 will be assumed.
To clear the list from the keypad, click [CLRMEM] and select "Stats".
Logistic Regression
Professional Edition Only. DreamCalc Professional offers a logistic regression mode (sometimes referred to as sigmoid regression). This fits an s-shaped curve to the data, and determines three coefficients, according to:
y = A / (1 + B.eC.x)
An example of a logistic curve fit is shown below.
In statistical analysis, the logistic curve is sometimes described by the formula:
P = 1 / (1 + e-(j+kx))
where P is a probability value between 0 and 1
and the relations:
P = y/A
j = -ln(B)
k = -C
translate the coefficients used in DreamCalc.
Performing Calculations: There are two ways to perform statistical calculations.
Using the List Window
Since DreamCalc version 4, statistical calculations are possible from the list page-tab of the Graphing & List Window.
Simply select from the Calc button drop-down menu to perform a calculation.
Using the Keypad
On the main keypad, you will find the following statistical keys:
- [S-SUM] (SumX, SumX2 etc.)
- [S-VAR] (MeanX, StdX[n], StdX[n-1] etc.)
- [S-DIST] (Coefficients and Variate Z etc.)
These keys allow input of statistical functions using an on-screen menu selection.
You can page through the available functions by pressing the respective key repeatedly. |
