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Analytics Lab

Advanced statistical analysis with p-values, regressions, and calculus

Analyze:

๐Ÿ“Š

No race data available. Generate demo data or log some laps to see analytics.

๐Ÿ“Š Descriptive Statistics

n={{ dataPoints.length }}
Mean (ฮผ)
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Median
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Std Dev (ฯƒ)
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Variance (ฯƒยฒ)
{{ formatNumber(descriptive.variance) }}
Std Error
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CV %
{{ formatNumber(descriptive.cv) }}%
Q1 (25th)
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Q2 (50th)
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Q3 (75th)
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{{ getDistributionEmoji() }}

{{ getDistributionName() }}

Skewness: {{ formatNumber(descriptive.skewness) }} | Kurtosis: {{ formatNumber(descriptive.kurtosis) }}

๐Ÿ“ˆ Regression Analysis

Trend Fitting
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Rยฒ (Linear)
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{{ getR2Label(regression.linear?.r2) }}
Slope (ฮฒโ‚)
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{{ regression.linear?.slope > 0 ? 'Increasing' : 'Decreasing' }} trend
t-Statistic
{{ formatNumber(regression.linear?.tStatistic, 3) }}
p-Value
{{ formatPValue(regression.linear?.pValue) }}
{{ regression.linear?.pValue < 0.05 ? 'โœ“ Statistically Significant (ฮฑ=0.05)' : 'โœ— Not Significant' }}
Polynomial (degree 2)
{{ regression.polynomial?.equation }}
Rยฒ (Polynomial)
{{ formatNumber(regression.polynomial?.r2, 4) }}

๐ŸŽฏ Confidence Intervals

Hypothesis Testing
95% Confidence Interval
[{{ formatNumber(ci95.lower) }}, {{ formatNumber(ci95.upper) }}]
Margin of Error: ยฑ{{ formatNumber(ci95.marginOfError) }}
90% CI Lower
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90% CI Upper
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99% CI Lower
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99% CI Upper
{{ formatNumber(ci99.upper) }}
First Half vs Second Half (t-test)
t-Statistic
{{ formatNumber(tTest.tStatistic, 3) }}
p-Value
{{ formatPValue(tTest.pValue) }}
Cohen's d
{{ formatNumber(tTest.effectSize, 3) }}
{{ tTest.effectSizeInterpretation }}
df
{{ formatNumber(tTest.degreesOfFreedom, 1) }}

โˆซ Calculus Analysis

Derivatives
โˆซ Total Area
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Cumulative sum
Avg Rate of Change
{{ formatNumber(calculus.avgRateOfChange, 2) }}%
Per lap
Max Derivative
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Steepest increase
Min Derivative
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Steepest decline
Inflection Points (f''(x) = 0)
{{ point.type === 'concave-up-to-down' ? 'โคต๏ธ' : 'โคด๏ธ' }} Lap {{ point.index + 1 }}: {{ formatNumber(point.value) }} {{ point.type === 'concave-up-to-down' ? 'Peak forming' : 'Recovery starting' }}
No inflection points detected
Local Maxima
{{ calculus.extrema?.maxima?.length || 0 }}
Local Minima
{{ calculus.extrema?.minima?.length || 0 }}

๐Ÿ”— Correlation Analysis

Pearson r
Variables r rยฒ p-value Strength
{{ corr.pair }} {{ formatNumber(corr.r, 3) }} {{ formatNumber(corr.r2, 3) }} {{ formatPValue(corr.pValue) }} {{ corr.interpretation }}
Key: r > 0 = positive correlation, r < 0 = negative correlation

โš ๏ธ Anomaly Detection

IQR Method
IQR
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Outliers Found
{{ outliers.length }}
Lower Fence
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Q1 - 1.5ร—IQR
Upper Fence
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Q3 + 1.5ร—IQR
Detected Outliers
Lap {{ outlier.index + 1 }} {{ formatNumber(outlier.value) }} z={{ formatNumber(outlier.zScore || outlier.deviation, 2) }}
โœ“ No statistical outliers detected

๐Ÿ“‰ Time Series Decomposition

Trend + Seasonal + Residual
Trend Strength
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Seasonal Strength
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Residual Variance
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Signal-to-Noise
{{ formatNumber(timeSeries.snr, 2) }} dB