> ## Documentation Index
> Fetch the complete documentation index at: https://docs.prepst.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Predictive Analytics

> Forecast learning outcomes with confidence intervals

## 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

```python theme={null}
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

```python theme={null}
{
    "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:

<Steps>
  <Step title="Data Collection">
    Collect all practice session scores over the last 60 days
  </Step>

  <Step title="Trend Analysis">
    Calculate linear trend using least squares regression
  </Step>

  <Step title="Projection">
    Extend trend line to target date
  </Step>

  <Step title="Confidence Intervals">
    Calculate prediction intervals based on historical variance
  </Step>
</Steps>

### Factors Influencing Predictions

<AccordionGroup>
  <Accordion title="Historical Trends">
    Recent performance trajectory heavily weights predictions. Accelerating students see upward projections.
  </Accordion>

  <Accordion title="Learning Velocity">
    Current velocity directly impacts predicted improvement rates.
  </Accordion>

  <Accordion title="Practice Frequency">
    More consistent practice leads to more reliable predictions and faster projected gains.
  </Accordion>

  <Accordion title="Cognitive Efficiency">
    Students with higher efficiency metrics progress faster than those with lower efficiency.
  </Accordion>
</AccordionGroup>

## Goal Tracking

### Setting Goals

Track progress toward specific score targets:

```python theme={null}
# 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

<ParamField name="Days to Goal" required>
  Estimated days until target score is reached
</ParamField>

<ParamField name="Progress Percent" required>
  Current progress toward goal as percentage
</ParamField>

<ParamField name="On Track Status" required>
  Boolean indicating whether trajectory will reach goal
</ParamField>

## Confidence Intervals

### Understanding Confidence Ranges

```python theme={null}
"confidence_intervals": {
    "math": {"low": 660, "high": 700},
    "rw": {"low": 620, "high": 660},
    "total": {"low": 1290, "high": 1350}
}
```

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

### 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

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

## Recommendations

The engine provides personalized study recommendations based on predictions:

```python theme={null}
recommendations = predictions['recommendations']

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

Example recommendations:

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

<Info>
  **Medium Priority**: Increase math practice frequency by 20%\
  **Expected Impact**: Accelerate trajectory by 5 days
</Info>

## Scenario Planning

### Optimistic Scenario

```python theme={null}
scenarios = predictions['scenarios']

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

### Conservative Scenario

```python theme={null}
print(f"Conservative: {scenarios['conservative']}")
# Assumes: Current pace continues
```

### Realistic Scenario

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

## Best Practices

<Tip>
  Review predictions weekly to track progress and adjust goals as needed.
</Tip>

<Warning>
  Don't make significant decisions based on predictions beyond 60 days. Short-term projections are more reliable.
</Warning>

<Info>
  Combine predictions with velocity analysis for the most complete picture of future performance.
</Info>

## 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

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

## Integration Example

```python theme={null}
# 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']
    }
```

## Next Steps

<CardGroup cols={2}>
  <Card title="Learning Velocity" icon="gauge" href="/guides/velocity">
    Understand how velocity powers predictions
  </Card>

  <Card title="API Reference" icon="code" href="/api/introduction">
    Explore the complete API documentation
  </Card>
</CardGroup>