# Example of a scatterplot with groups and fitted regression lines

A quality engineer for a camera manufacturer wants to shorten the flash recovery time. Flash recovery time is the least amount of time that is required between flashes. The engineer wants to determine whether a relationship exists between the voltage that remains in the camera battery immediately after a flash and the flash recovery time. The engineer also wants to determine whether there are differences in flash recovery time between old and new formulations of the battery. The engineer collects random samples of batteries made with the old and new formulations. The engineer measures the volts remaining immediately after a flash and the flash recovery time for each.

As part of the initial investigation, the engineer creates a scatterplot of volts after versus flash recovery time, grouped by battery formulation, to assess the relationship between the two variables for the two formulations.

1. Open the sample data, FlashRecoveryTime.MTW.
2. Choose Graphs > Scatterplot > Single Y Variable: With Groups.
3. In Y variable, enter Flash Recovery.
4. In X variable, enter Volts After.
5. In Group variable, enter Formulation.
6. Click OK.
7. Click the graph to select it, then click the plus sign beside the graph to open the Graph Elements menu.
8. Select Regression Fit. To change the model for the regression lines, click the triangle next to Regression Fit ( ). For more information on regression models, go to Customize the scatterplot.

## Interpret the results

Minitab calculates a separate regression equation for each group. The regression lines suggest that, within the range of voltages tested, recovery times for the new formulation are generally faster than the recovery times for the old formulation. The regression lines and equations suggest a negative linear relationship between recovery time and voltage for both groups. On average, with an increase of 1 volt, recovery time of the new batteries is reduced by approximately 2.7 seconds. For the old formulation, the recovery time is reduced by approximately 3.9 seconds.

 Summary Statistics
 Variable Formulation N Mean StDev Minimum Maximum Flash Recovery New 20 4.8125 0.5888 3.7000 5.6100 Old 20 5.9870 0.8344 4.4900 7.1600 Volts After New 20 1.19760 0.12076 0.99000 1.45600 Old 20 1.18555 0.13051 0.96700 1.44900
 Regression
 Formulation R-sq Equation New 30.64% Flash Recovery = 8.04507 − 2.69921 Volts After Old 37.20% Flash Recovery = 10.6095 − 3.89908 Volts After
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