# Fitted Line Plot

## Summary

A simple regression tool used to plot one Y versus one X to evaluate linear, quadratic, or cubic relationships. The best fit regression line is displayed with optional confidence and prediction intervals around the fitted regression line. The confidence interval is for the regression equation and the prediction interval is for the individual points.

• Is any relationship between two variables, Y and X, apparent?
• How strong is the relationship between Y and X?
• What value of a process input X results in the optimal process output Y?
When to Use Purpose
Start of project Compare a proposed or existing gage to a highly qualified device (such as a certified lab). A high r-squared (R-Sq) value provides reasonable certainty of the test gage matching the reference gage.
Start of project Use to help develop alternative measurement systems for cases in which a variable is difficult or expensive to measure. Use highly correlated and logically linked alternative variables as substitute variables.
Mid-project Investigate the relationship between a process input and the process output to help decide to either keep the input as a potential leverage variable or set it aside as most likely not important.
Mid-project Evaluate two inputs to identify whether they duplicate the same information. For example, inputs of Degree Obtained and Years of School are likely to explain the same variation of the output, so one of them can be eliminated. This is used primarily in multiple regression analysis with many variables.
End of project Verify the measurement system. If you use a fitted line plot earlier as part of the validation of the measurement system, create another one with the improved process to again validate the measurement system.

### Data

Continuous Y with one continuous or discrete X (with multiple levels)

## How-To

1. Collect data from your process over its expected range of input values. Enter the input values into one column and the output into a second column.
2. Select either a linear, quadratic, or cubic analysis.
3. You can also add confidence and/or prediction intervals around the regression line.

## Guidelines

• Samples should be taken across the entire inference space. Do not extrapolate by using the equation to predict Y values outside the range of sampled X's. The graphical output also helps identify outliers.
• The residuals must be independent, reasonably normal, and have reasonably equal variances. The fitted line plot uses regression, which is quite robust to nonnormality. Analyze the residuals using a histogram, normal probability plot, plot versus fits, and plot versus order, which can be run at one time using the Four-in-one option.
• If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.
By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy