Overview
Statistics worksheet can provide one variable analysis as well as two variable regressions. Below is a table of labels & variables that the statistics worksheet contain and their meanings.
| Label | Definition |
|---|---|
| Xn | The nth value in sequence X |
| Yn | The nth value in sequence Y |
| LIN | Linear Regression |
| Ln | Logarithmic Regression |
| EXP | Exponential Regression |
| PWR | Power Regression |
| 1-V | One-variable statistics |
| n | # of observation |
| x̄ | Mean/Average of X |
| Sx | Sample standard deviation of X |
| σx | Population standard deviation of X |
| ȳ | Mean/Average of Y |
| Sy | Sample standard deviation of Y |
| σy | Population standard deviation of Y |
| a | Intercept of regression |
| b | Slope of regression |
| r | Correlation coefficient |
| X’ | Predicted X value |
| Y’ | Predicted Y value |
| ΣX | Sum of X values |
| ΣX2 | Sum of X squared values |
| ΣY | Sum of Y values |
| ΣY2 | Sum of Y squared values |
| ΣXY | Sum of XY products |
Regression Models
The four types of regression are Linear, Logarithmic, Exponential and Power Regression.
| Model | Formula |
|---|---|
| Linear | Y = a + bX |
| Logarithmic | Y = a + bln(X) |
| Exponential | Y = abX |
| Power | Y = aXb |
Example: One Variable
Provide # of observation, mean, sample standard deviation, population standard deviation, sum and sum of squaredness for the following one variable series.
| X | 1 | 2 | 3 | 4 | 5 |
First, you need to enter the data set.
| Keystrokes | Display | |
|---|---|---|
| 2ND Data | X1 | 0 |
| 1 ENTER | X1 = | 1 |
| ▶ | Y1 = | 1 |
| ▶ 2 ENTER | X2 = | 2 |
| ▶ | Y2 = | 1 |
| ▶ 3 ENTER | X3 = | 3 |
| ▶ | Y3 = | 1 |
| ▶ 4 ENTER | X4 = | 4 |
| ▶ | Y4 = | 1 |
| ▶ 5 ENTER | X5 = | 5 |
| ▶ | Y5 = | 1 |
Then you can show statistical analysis.
| Keystrokes | Display | |
|---|---|---|
| 2ND STAT | LIN | |
| 2ND SET | 1-V | |
| ▶ | n = | 5 |
| ▶ | x̄ = | 3 |
| ▶ | Sx = | 1.58113883 |
| ▶ | σx = | 1.414213562 |
| ▶ | ΣX = | 15 |
| ▶ | ΣX2 = | 55 |
Example: Linear Regression
Provide linear regression results given the following dependent variable Y and independent variable X. Predict Y’ given X’=6.
| X | 1 | 2 | 3 | 4 | 5 |
| Y | 2 | 3.5 | 5.8 | 8 | 10.2 |
Enter the data set.
| Keystrokes | Display | |
|---|---|---|
| 2ND Data | X1 | 0 |
| 1 ENTER | X1 = | 1 |
| ▶ 2 ENTER | Y1 = | 2 |
| ▶ 2 ENTER | X2 = | 2 |
| ▶ 3.5 ENTER | Y2 = | 3.5 |
| ▶ 3 ENTER | X3 = | 3 |
| ▶ 5.8 ENTER | Y3 = | 5.8 |
| ▶ 4 ENTER | X4 = | 4 |
| ▶ 8 ENTER | Y4 = | 8 |
| ▶ 5 ENTER | X5 = | 5 |
| ▶ 10.2 ENTER | Y5 = | 10.2 |
Show regression results.
| Keystrokes | Display | |
|---|---|---|
| 2ND STAT | LIN | |
| ▶ | n = | 5 |
| ▶ | x̄ = | 3 |
| ▶ | Sx = | 1.58113883 |
| ▶ | σx = | 1.414213562 |
| ▶ | ȳ = | 5.96 |
| ▶ | Sy = | 3.410718399 |
| ▶ | σy = | 3.050639277 |
| ▶ | a = | -0.49 |
| ▶ | b = | 2.15 |
| ▶ | r = | 0.996695736 |
| ▶ 6 ENTER | X’ = | 6 |
| ▶ CPT | Y’ = | 12.41 |
| ▶ | ΣX = | 15 |
| ▶ | ΣX2 = | 55 |
| ▶ | ΣY = | 29.8 |
| ▶ | ΣY2 = | 224.14 |
| ▶ | ΣXY = | 110.9 |
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