To enter the **Regression** application, highlight the app using the directional keys. Press the ** ok** key to enter the application. This application allows you to perform statistical computations on two-dimensional data sets.

When you enter the **Regression** app, you must enter your data into a two-column table. You may add up to 3 data tables.

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

Once you have entered your data into the table, you may view a scatterplot of your data. To do this:

- Highlight the
**Graph**tab at the top of the screen. - Confirm with the
key.*ok*

You will see the points that represent your data. The coordinates of the selected point will be displayed in the bottom banner along with the correlation coefficent, r.

Once you have created a scatterplot, you may plot a regression model. To do this:

- While on the
**Graph**tab, press thekey to view a list of regression model options.*ok* - Highlight the model you would like to use.
- Confirm with the
key.*ok*

You can now use the ** down**/

Once you have entered your data into the table in the **Data** tab, you may view the statistical values: mean, standard deviation, median, etc.

- Highlight the
**Stats**tab at the top of the screen. - Confirm with the
key. You will see the table of statistical values.*ok*

To clear an element from a data table:

- Highlight the cell that you wish to clear.
- Press the
key. The cell has been cleared.*del*

To change a value, highlight the desired cell and enter a new value with the numerical keys.

You may clear an entire column from any data table. To clear an entire column from a data table:

- Highlight the name of the column you want to clear. For example, highlight
**X1**to clear the first column of the first data table. - Confirm by pressing the
key. The column options menu will open.*ok* - Highlight
**Clear column**. - Confirm with the
key. The column has been cleared.*ok*

You can also clear a column by pressing the

key when a column name is highlighted.del

You may fill a column of a data table using a formula. To fill a column with a formula:

- Highlight the name of the column you wish to fill. For example, highlight
**Y1**. - Confirm by pressing the
key.*ok* - The column options menu opens. Highlight
**Fill with formula**. - Confirm with the
key.*ok* - Select a list function from the templates or use the
**Empty**template to create your own. - You can also enter a formula using the name of another column. For example, if you would like column
**Y1**to be filled with the values of**X1**divided by 2, write`X1/2`

in the editing field at the bottom of the screen. - Confirm with the
key.*ok*

You can re-evaluate or edit the formula by returning to the

Fill with formulaoption.

You may sort a list in a data table by increasing values.

- Highlight the name of the column you would like to sort.
- Confirm with the
key.*ok* - The column options menu opens. Highlight
**Sort by increasing values**. - Confirm with the
key. The items of your list have been sorted.*ok*

You may change the regression model you’ll use directly in the Data tab.

To change the regression model you are using:

- Highlight the name of a column.
- Confirm with the
key. The options menu will open.*ok* - Highlight
**Model**. - Confirm with the
key.*ok* - Highlight your desired model.
- Confirm with the
key.*ok*

You may adjust the display window in the **Graph** tab to fit your needs. This includes: editing your X and Y values, zooming in and out, and more. There are three menus that allow you to adjust your graphing window: **Auto**, **Axes** and **Navigate**. To adjust your graphing window:

- Highlight your desired menu. The menus are located underneath the tabs near the top of the screen.
- Confirm by pressing the
key.*ok*

You may press

andplusto zoom in/out while in theminusGraphtab.

The NumWorks graphing calculator will adapt to display the best possible view of your regression. Once you enter your data, the resulting axes will be chosen automatically. When **Auto** is active, a yellow circle will appear to the right of its name. Once you exit this window, either with the directional keys or by changing the settings, Auto will be disabled and the yellow circle will disappear.

You may also highlight

Autoand press thekey to disabled theokAutomode.

The **Axes** menu allows you to make manual changes to the axes of your graphing window. To make changes to the X or Y values:

- Highlight
**Axes**. - Press the
key to enter the menu.*ok* - Highlight
**Values of X**or**Values of Y** - Confirm with the
key.*ok* - Enter your desired
**Minimum**and**Maximum**values. To allow the calculator to choose automatically, select**Auto**at the top of the screen. - Highlight
**Confirm**at the bottom of the screen. - Confirm with the
key.*ok*

You may make your axes equal inside the **Axes** menu. To do this, highlight **Make axes equal** and confirm with the ** ok** key. Selecting this option will lengthen the shortest axis to match the longest. When your axes are not equal, a symbol will appear beside the

Select **Navigate** to work with the interactive display window:

/*left*/*up*/*right*: move the window*down*/*plus*: zoom in/zoom out*minus*

You can move the cursor using the four directional arrows:

/*left*: move the cursor from point to point.*right*/*up*: move the cursor from the data points of one set to another data set.*down*

Once you have created a scatterplot, you may plot a regression model. To do this:

- Open the
**Regression**menu. - Highlight the regression model you would like to use.
- Confirm with the
key.*ok*

You can now use the ** up**/

Once a model regression model is selected, the equation of the model can be accessed in other applications from within the

varmenu.

Once a regression model has been plotted, you can view additional information about the model in the **Regression** menu including:

- the regression equation
- the correlation coefficent (for linear models only)
- the coefficient of determination, $r^2$

The **Regression** menu also gives you access to a residual plot. To view the residual plot:

- Open the
**Regression**menu. - Navigate down to
**Residual plot**. - Confirm with the
key.*ok*

You can now use the ** left**/

You may look for a specific point on the regression model for a given x or predicted y value. In other words, you may predict a value of $Y$ given $X$ and a determine the value of $X$ needed for a given predicted $Y$.

- Open the
**Regression**menu. - Navigate down to
**Predict Y given X**if you know the value of $X$ or**Find X given predictd Y**if you want to know the value of $X$ given a predicted $Y$. - Confirm with the
key.*ok* - Enter your value.
- Highlight
**Confirm**. - Press the
key.*ok*

The cursor will move to the desired point. You may view the coordinates of this point at the bottom of the screen.

You may change the regression model you use. The available models are:

- Linear
`ax + b`

- Linear
`a + bx`

- Proportional
- Quadratic
- Cubic
- Quartic
- Logarithmic
- Exponential
`a*b^x`

- Exponential
`a*e^(bx)`

- Power
- Trigonometric
- Logistic
- Median-Median

To change the regression model you are using:

- Open the
**Regression**menu. - While highlighting
**Model**, confirm with thekey.*ok* - Highlight your desired model.
- Confirm with the
key. You have now changed the regression model.*ok*

You may remove a regression model from the scatterplot. To remove the regression model:

- Open the
**Regression**menu. - Navigate to
**Remove regression**. - Confirm with the
key.*ok*

The **Stats** tab displays statistical variables calculated using the data in the **Data** tab. The following datas are calculated:

- Mean of $x_{i}$ 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 $y_{i}$
- Sample standard deviation of $x_{i}$ and $y_{i}$
- Number of data points
- Covariance
- Sum of $x_{i} \times y_{i}$

If a model has been plotted, the **Stats** tab will also display:

- Correlation coefficient $r$ (for linear models)
- Regression equation
- Regression equation parameters
- Residual standard deviation
- Coefficient of determination $r^2$