Scatter diagram & regression line

Command:

Statistics Regression Scatter diagram & regression line

Description

In a scatter diagram, the relation between two numerical variables is presented graphically. One variable (the independent variable X) defines the horizontal axis and the other (dependent variable Y) defines the vertical axis. The values of the two variables on the same row in the data spreadsheet, give the points in the diagram.

Required input

The dialog box for the scatter diagram is similar to the one for Regression:

The regression curve will be drawn in the diagram. The equation of this curve is given in the Regression results window. When you select an equation that contains a logarithmic transformation for one or both of the variables, the program will use a logarithmic scale for the corresponding variable(s).

Finally, you can select 2 options:

95% Confidence: when you select this option then two curves will be drawn parallel to the regression line. These curves represent a 95% confidence interval for the regression line. This interval includes the true regression line with 95% probability.

95% Prediction: when you select this option then two curves will be drawn parallel to the regression lines. These curves represent the 95% prediction interval for the regression curve. The 95% prediction interval is much wider than the 95% confidence interval. For any given value of the independent variable, this interval represents the 95% probability for the values of the dependent variable.

Scatter diagram with regression line

Regression line and 95% confidence interval

Regression line and 95% prediction interval

Regression line, 95% confidence interval and 95% prediction interval

When you click a point on the regression line, the program will give the x-value and the f(x) value calculated using the regression equation.

You can press Ctrl+P to print the scatter diagram, or function key F10 to save the picture as file on disk. To define other titles or colors in the graph, or change the axis scaling, see Format graph.

If you want to repeat the scatter diagram, possibly to select a different regression equation, then you only have to press function key F7. The dialog box will re-appear with the previous entries (see F7 - Repeat key).

Extrapolation

MedCalc does only show the regression line in the range of observed values. As a rule, it is not recommended to extrapolate the regression line beyond the observed range. For particular applications however, such as evaluation of stability data, extrapolation may be useful, see for example the ICH guideline Evaluation of Stability Data (PDF).

To allow extrapolation, right-click in the graph and select Allow extrapolation in the popup menu.

Residuals plot

When you select the option Residuals plot in the Regression line dialog box, the program will display a second window with the residuals plot. Residuals are the differences between the predicted values and the observed values for the dependent variable. The residual plot allows for the visual evaluation of the goodness of fit of the selected model or equation. Residuals may point to possible outliers (unusual values) in the data or problems with the regression model. If the residuals display a certain pattern, you should consider to select a different regression model.

Literature

• Altman DG (1991) Practical statistics for medical research. London: Chapman and Hall.

See also

• Regression
• Format graph
• Graph legend
• Add graphical objects
• Reference lines