1. Objective: Conduct a regression analysis to determine effective battery capacity based on:
End of Life Cell Voltage
Peak Current
Daily Battery Consumption
The table to the left contains the data used for this analysis.
Problem Setup
3 Variables
4 Levels for each variable
Creates a 43 matrix (64 data points)

2. The raw data shown on the left represents the 64 data points in a structured sequence for use in MiniTab
A Main Effects Plot was run to determine if any of the variables were of little consequence or behaved in an unusual manner
Data shows that each variable is important
All variables have a negative impact on capacity
Relationships are fairly linear

3. Histogram shows the distribution of the 64 data points

4. The regression equation is
A Regression Analysis was run and showed a fairly good correlation R2 of 98% with the linear equation shown.
The regression equation is
mAH = Peak Current EoL Voltage Daily Pwr
Predictor Coef SE Coef T P
Constant
Peak Cur
EoL Volt
Daily Pw
S = R-Sq = 98.0% R-Sq(adj) = 97.9%
R Unusual Observations
Obs Peak Cur mAH Fit SE Fit Residual St Resid R R R
The equation starts to fall apart toward the extremes

5. To achieve better accuracy, the outliers highlighted in yellow were removed from the analysis.

6. The correction is slighter better with the outliers removed
The correction is slighter better with the outliers removed. The equation is still linear.
Conclusion: Not worth removing the data points.
The regression equation is
mAH = Peak Current EoL Voltage Daily Pwr
Predictor Coef SE Coef T P
Constant
Peak Cur
EoL Volt
Daily Pw
S = R-Sq = 99.1% R-Sq(adj) = 99.0%

7. Random Check
Peak Current
EoL Voltage
Daily Pwr Cons
Calculated
Actual
Difference mA V
mAh/day
mAh
500 1 2
2611.5
2642
1.2%
1.1 4
2076
2057
-0.9%
1000
1.2
2008
1972
-1.8%
2159.5
2126
-1.6%
1500 3
1579.5
1615
2.2%
2010.5
1990
-1.0%
2000
0.9
2373.5
2351
1686.5
1698
0.7%
Capacity(mAh) = Peak(mA) – 2795EoL(V) Daily(mAh/day)
Randomly checking a few data points, the calculated numbers are within 2% of the data provided.
Worst Case shows 5.7% under-reporting of battery capacity compared to provided data