# Regression

## Getting started

### Typing your data in the table

When you enter the Regression app, you must type your data in a two-column table. You can add up to 3 data tables.

• In the first column (X1), enter the values of the first variable of your statistical data set.
• In the second column (Y1), enter the values of the second variable of your statistical data set.

### Computing the linear regression

Once you have entered your data in the table, you can plot a linear regression.

1. Select the Graph tab at the top of the screen.
2. Confirm by pressing ok.

You then see the points that represent your data as well as the regression line that fits the model equation $y=ax+b$. The $a$ and $b$ coefficients are displayed in the banner at the bottom of the screen.

### Displaying statistical variables

Once you have typed your data into the table in the Data tab, you can display the statistical variables: mean, standard deviation, median,…

1. Select the Stats tab at the top of the screen.
2. Confirm by pressing ok.

You then see the table of statistical variables.

## Using the Data tab

### Delete a value from the data table

You can delete a row from the table by selecting a cell in that row and pressing del.

You can change the content of a cell by selecting it and typing a new value with the keyboard.

### Clearing a column of the table

You can delete all the values in a column of the table.

1. Select the name of the column you want to clear. Confirm by pressing ok.
2. The column options menu opens. Select Clear column and confirm with ok.

Clearing the $x_{i}$ column also clears the $y_{i}$ column.
Clearing the $y_{i}$ column fills this column with the value $0$.

### Generate a list with a formula

You can create a column of the data table using a formula involving another column.

1. Select the name of the column you want to fill. Confirm by pressing ok.
2. The column options menu opens. Select Fill with formula and confirm with ok.
3. Type your formula using the name of another column. For example, if you want column X2 to be filled with the values of X1 divided by 2, write X1/2 in the text field at the bottom of the screen. Then press OK.

To enter a capital letter, press shift then alpha then the letter to display.

You can change the regression adjustment to use. The available adjustments are:

• Linear
• Cubic
• Quartic
• Logarithmic
• Exponential
• Power
• Trigonometric
• Logistic
1. Select the name of a column and confirm by pressing ok.
2. The column options menu opens. Select Regression and confirm with ok.

## Using the Graph tab

### Moving the cursor in the graph window

You can move the cursor using the four directional arrows:

• left / right: move the cursor on the line to the right or left or from point to point.
• up / down: move the cursor from the data points to the regression line or move to another data set.

### Predict a value of X or Y

You can look for a specific point on the regression line knowing its abscissa or ordinate: that is, you can predict a value of $X$ given $Y$ and a value of $Y$ given $X$.

1. Move the cursor to the regression line and press ok.
2. The regression line menu opens. Select Prediction given X if you know the value of $X$ and Prediction given Y if you know the value of $Y$. Confirm by pressing ok.
3. Type your value, then select the Validate button and press ok.

The cursor has moved to the desired point. You can read the coordinates of this point at the bottom of the screen.

You can change the regression adjustment to use. The available adjustments are:

• Linear
• Cubic
• Quartic
• Logarithmic
• Exponential
• Power
• Trigonometric
• Logistic
1. Move the cursor to a curve and press ok.
2. The curve options menu opens. Select Regression and confirm with ok.

To access the display window settings, select one of the options under the Graph tab and press ok.
You can choose between three options: Axes, Zoom and Preadjustment.

When you are in the graph display window, you can press the + and - keys to zoom in/out.

#### Axes

In Axes, you can enter the values of Xmin and Xmax that define the width of your display window.

If Yauto is activated, the height of your display window will be automatically calculated to display all points of the curve between Xmin and Xmax. Otherwise, manually enter your Ymin and Ymax values.

Confirm by selecting the Confirm button and pressing ok.

#### Zoom

Select Zoom to access an interactive display window setting:

• left / up / right / down: move the window
• + / -: zoom in/zoom out

• Integer: window in which the abscissa are integers
• Orthonormal: window displaying an orthonormal coordinate system
• Basic settings: reset the display window

## Using the Stats tab

The Stats tab displays the statistical variables calculated using the data in the Data tab:

• Mean of $x_{i}$ values and $y_{i}$
• Sum of $x_{i}$ and $y_{i}$
• Sum of the squares of $x_{i}$ and $y_{i}$
• Standard deviation of $x_{i}$ and $y_{i}$
• Variance of $x_{i}$ and $y_{i}$
• Number of data points
• Covariance
• Sum of $x_{i} \times y_{i}$
• Slope $a$ and y-intercept $b$ of the regression line (or other adjustment coefficients)
• Correlation coefficient $r$
• Coefficient of determination $r^2$