Predictive Analytics

Overview

The Cognitive Learning Engine uses advanced predictive analytics to forecast student performance, estimate goal achievement timelines, and provide data-driven study recommendations.

Score Predictions

Basic Usage

from cognition_engine import CognitionEngine

engine = CognitionEngine(supabase_url, supabase_key)

# Get predictions
predictions = await engine.get_predictions("student_123")

print(f"Current SAT Math: {predictions['current_math']}")
print(f"Predicted SAT Math in 30 days: {predictions['predicted_math_in_30_days']}")
print(f"Goal progress: {predictions['goal_progress_percent']}%")

Prediction Response

{
    "current_math": 620,
    "current_rw": 580,
    "current_total": 1200,
    "predicted_math_in_30_days": 680,
    "predicted_rw_in_30_days": 640,
    "predicted_total_in_30_days": 1320,
    "confidence_intervals": {
        "math": {"low": 660, "high": 700},
        "rw": {"low": 620, "high": 660},
        "total": {"low": 1290, "high": 1350}
    },
    "goal_tracking": {
        "target_score": 1400,
        "days_to_goal": 45,
        "progress_percent": 75,
        "on_track": True
    }
}

How Predictions Work

Linear Regression Model

Predictions use linear regression based on historical performance trends:

Data Collection

Collect all practice session scores over the last 60 days

Trend Analysis

Calculate linear trend using least squares regression

Projection

Extend trend line to target date

Confidence Intervals

Calculate prediction intervals based on historical variance

Factors Influencing Predictions

Historical Trends

Recent performance trajectory heavily weights predictions. Accelerating students see upward projections.

Learning Velocity

Current velocity directly impacts predicted improvement rates.

Practice Frequency

More consistent practice leads to more reliable predictions and faster projected gains.

Cognitive Efficiency

Students with higher efficiency metrics progress faster than those with lower efficiency.

Goal Tracking

Setting Goals

Track progress toward specific score targets:

# Student wants 1400 total SAT score
goal_tracking = predictions['goal_tracking']

if goal_tracking['on_track']:
    print(f"On track! {goal_tracking['days_to_goal']} days to goal")
else:
    print(f"Need to accelerate by {goal_tracking['acceleration_needed']}")

Goal Metrics

Confidence Intervals

Understanding Confidence Ranges

"confidence_intervals": {
    "math": {"low": 660, "high": 700},
    "rw": {"low": 620, "high": 660},
    "total": {"low": 1290, "high": 1350}
}

Confidence intervals represent the range where we expect the actual score to fall with 95% probability. Narrower intervals indicate more reliable predictions.

Factors Affecting Confidence

Sample size: More data = narrower intervals
Consistency: Steady progress = more confidence
Recency: Recent data weighted more heavily
Variability: Lower variance = tighter estimates

Predictions become less reliable beyond 60 days. Always use recent velocity data for long-term projections.

Recommendations

The engine provides personalized study recommendations based on predictions:

recommendations = predictions['recommendations']

for rec in recommendations:
    print(f"{rec['priority']}: {rec['action']}")
    print(f"Expected impact: {rec['impact']}")

Example recommendations:

High Priority: Focus on Reading/Writing fundamentals - largest growth opportunity
Expected Impact: +25 points in 30 days

Medium Priority: Increase math practice frequency by 20%
Expected Impact: Accelerate trajectory by 5 days

Scenario Planning

Optimistic Scenario

scenarios = predictions['scenarios']

print(f"Optimistic: {scenarios['optimistic']}")
# Assumes: Increased practice, improved efficiency

Conservative Scenario

print(f"Conservative: {scenarios['conservative']}")
# Assumes: Current pace continues

Realistic Scenario

print(f"Realistic: {scenarios['realistic']}")
# Most likely outcome based on current trajectory

Best Practices

Review predictions weekly to track progress and adjust goals as needed.

Don’t make significant decisions based on predictions beyond 60 days. Short-term projections are more reliable.

Combine predictions with velocity analysis for the most complete picture of future performance.

Limitations

What Predictions Can’t Account For

Life events: Unexpected disruptions to study routine
Curriculum changes: New topics not yet practiced
Motivation shifts: Changes in student engagement
Test anxiety: Performance under pressure vs. practice

Improving Prediction Accuracy

More practice data: Aim for 50+ sessions per subject
Consistent frequency: Regular practice improves reliability
Recent updates: Keep velocity current with fresh data
Diverse problems: Mix difficulty levels and topics

Integration Example

# Dashboard integration
async def get_student_dashboard(user_id):
    predictions = await engine.get_predictions(user_id)
    velocity = await engine.get_learning_velocity(user_id)
    
    return {
        "current_score": predictions['current_total'],
        "predicted_score": predictions['predicted_total_in_30_days'],
        "goal_progress": predictions['goal_tracking']['progress_percent'],
        "momentum": velocity['momentum_score'],
        "recommendations": predictions['recommendations']
    }

Getting Started

Core Concepts

Advanced Topics

Overview

Score Predictions

Basic Usage

Prediction Response

How Predictions Work

Linear Regression Model

Factors Influencing Predictions

Goal Tracking

Setting Goals

Goal Metrics

Confidence Intervals

Understanding Confidence Ranges

Factors Affecting Confidence

Recommendations

Scenario Planning

Optimistic Scenario

Conservative Scenario

Realistic Scenario

Best Practices

Limitations

What Predictions Can’t Account For

Improving Prediction Accuracy

Integration Example

Next Steps

Learning Velocity

API Reference

​Overview

​Score Predictions

​Basic Usage

​Prediction Response

​How Predictions Work

​Linear Regression Model

​Factors Influencing Predictions

​Goal Tracking

​Setting Goals

​Goal Metrics

​Confidence Intervals

​Understanding Confidence Ranges

​Factors Affecting Confidence

​Recommendations

​Scenario Planning

​Optimistic Scenario

​Conservative Scenario

​Realistic Scenario

​Best Practices

​Limitations

​What Predictions Can’t Account For

​Improving Prediction Accuracy

​Integration Example

​Next Steps

Learning Velocity

API Reference

Overview

Score Predictions

Basic Usage

Prediction Response

How Predictions Work

Linear Regression Model

Factors Influencing Predictions

Goal Tracking

Setting Goals

Goal Metrics

Confidence Intervals

Understanding Confidence Ranges

Factors Affecting Confidence

Recommendations

Scenario Planning

Optimistic Scenario

Conservative Scenario

Realistic Scenario

Best Practices

Limitations

What Predictions Can’t Account For

Improving Prediction Accuracy

Integration Example

Next Steps