Statistical analysis of my laptop battery health over time using Windows battery report data.
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Because the data are time-ordered, residuals exhibit strong positive autocorrelation (Durbin–Watson ≈ 0.13). This behavior is expected in cumulative degradation processes. Therefore, standard errors from OLS may be underestimated.
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The slope is interpreted primarily as an average degradation rate rather than a strict inferential result.
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Using the OLS estimated slope, we estimate that battery health degrades over time at a rate of:
- a) ~0.022% per day.
- b) ~0.155% per week.
- c) ~0.66% per month.
- d) ~8.1% per year.
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Using the GLS estimated slope, we estimate that battery health degrades over time at a rate of:
- a) ~0.0193% per day.
- b) ~0.135% per week.
- c) ~0.58% per month.
- d) ~7.0% per year.
Under OLS, battery health was estimated to decline at approximately 0.022% per day (≈8.1% per year). After accounting for strong positive autocorrelation using a GLS model with AR(1) errors, the estimated degradation rate decreased slightly to approximately 0.019% per day (≈7.0% per year). While GLS yields a more conservative estimate with larger standard errors, the magnitude and direction of the degradation trend remain consistent across models, indicating that the observed battery health decline is robust to autocorrelation effects.