# Regression

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.

## Getting started

### Entering your data into the table

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.

### Viewing a scatterplot

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

1. Highlight the Graph tab at the top of the screen.
2. Confirm with the ok key.

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.

### Plotting a regression model

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

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

You can now use the down/up keys to move from a data point to the regression model. When the model is select, the bottom banner will include the predicted value and the equation.

### Displaying statistical values

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

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

## Using the Data tab

### Clearing an element from a data table

To clear an element from a data table:

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

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

### Clearing a column from a data table

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

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

You can also clear a column by pressing the del key when a column name is highlighted.

### Generating a list with a formula

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

1. Highlight the name of the column you wish to fill. For example, highlight Y1.
2. Confirm by pressing the ok key.
3. The column options menu opens. Highlight Fill with formula.
4. Confirm with the ok key.
5. Select a list function from the templates or use the Empty template to create your own.
6. 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.
7. Confirm with the ok key.

You can re-evaluate or edit the formula by returning to the Fill with formula option.

### Sorting a list by increasing values

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

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

### Changing the regression model in the Data tab

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

To change the regression model you are using:

1. Highlight the name of a column.
2. Confirm with the ok key. The options menu will open.
3. Highlight Model.
4. Confirm with the ok key.
6. Confirm with the ok key.

## Using the Graph tab

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:

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

You may press plus and minus to zoom in/out while in the Graph tab.

#### Auto

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 Auto and press the ok key to disabled the Auto mode.

#### Axes

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:

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

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 Axes menu.

Select Navigate to work with the interactive display window:

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

You can move the cursor using the four directional arrows:

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

### Regression

#### Plotting a regression model

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

2. Highlight the regression model you would like to use.
3. Confirm with the ok key.

You can now use the up/down keys to move from a data point to the regression model. When the model is select, the bottom banner will include the predicted value and the equation.

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

#### Viewing regression information

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, $r^2$

#### Viewing a residual plot

2. Navigate down to Residual plot.
3. Confirm with the ok key.

You can now use the left/right keys to move the cursor to view data points and their corresponding residual value.

#### Making predictions

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 $Y$.

2. 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 $Y$.
3. Confirm with the ok key.
5. Highlight Confirm.
6. Press the ok key.

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

#### Changing the regression model

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

• Linear ax + b
• Linear a + bx
• Proportional
• Cubic
• Quartic
• Logarithmic
• Exponential a*b^x
• Exponential a*e^(bx)
• Power
• Trigonometric
• Logistic
• Median-Median

To change the regression model you are using:

2. While highlighting Model, confirm with the ok key.
4. Confirm with the ok key. You have now changed the regression model.

#### Removing a regression

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

2. Navigate to Remove regression.
3. Confirm with the ok key.

## Using the Stats tab

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 $r^2$