AVM (Automated Valuation Model)

A computer program that uses data and statistical methods to estimate property values without human input.

Confidence Score

A percentage showing how reliable the model thinks its estimate is. Higher percentages mean the model is more confident.

$$\text{Confidence Score} = 100 - \text{Median MAPE}$$

The confidence score is calculated by subtracting the model's median MAPE from 100%. For example, if the median MAPE is 8%, the confidence score would be 92%. This means the model is typically accurate within 8% of the actual value, so we can be 92% confident in its predictions.

Training vs Testing Data

The model learns from training data, then its accuracy is tested on separate data it hasn't seen before. Testing results are more reliable indicators of real-world performance.

R-squared (Coefficient of Determination)

A measure of how well the model explains property values. Values range from 0 to 1, with values closer to 1.0 meaning the model is better at predicting prices.

$$R^2 = 1 - \frac{SS_{res}}{SS_{tot}}$$

Where SS_res is the sum of squares of residuals and SS_tot is the total sum of squares.

Mean Absolute Error (MAE)

The average difference between the model's predictions and actual sale prices. Lower values mean more accurate predictions.

$$MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i|$$

Where y_i is the actual value, ŷ_i is the predicted value, and n is the number of predictions.

Root Mean Square Error (RMSE)

Similar to MAE but gives more weight to larger errors. Lower values indicate better accuracy.

$$RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}$$

The square root of the average of squared differences between actual and predicted values.

MAPE (Mean Absolute Percentage Error)

The average percentage difference between predicted and actual values. Lower percentages mean better accuracy.

$$MAPE = \frac{1}{n} \sum_{i=1}^{n} \left|\frac{y_i - \hat{y}_i}{y_i}\right| \times 100\%$$

Shows error as a percentage of the actual value, making it easier to interpret across different price ranges.

Median MAPE

The middle value when all percentage errors are sorted from lowest to highest. Less affected by extreme errors than regular MAPE.

Often provides a better sense of typical prediction accuracy than the mean.

Within X% Accuracy

The percentage of predictions that were within X% of the actual sale price. Higher percentages are better.

$$\text{Within X%} = \frac{\text{Count of } |\text{error}| \leq X\% \text{ of actual}}{\text{Total predictions}} \times 100\%$$

For example, 'Within 10%' means what percentage of predictions were within 10% of the actual sale price.

Mean Bias

Whether the model tends to predict prices too high (positive bias) or too low (negative bias) on average. Values closer to zero are better.

$$\text{Mean Bias} = \frac{1}{n} \sum_{i=1}^{n} (\hat{y}_i - y_i)$$

Positive values mean the model overestimates, negative values mean it underestimates.

Median Bias

The middle value of all prediction errors when sorted. Less affected by extreme errors than mean bias.

Provides a better sense of typical model behavior than mean bias.

Over-prediction Rate

The percentage of times the model predicted higher than the actual sale price.

$$\text{Over-prediction Rate} = \frac{\text{Count of } \hat{y}_i > y_i}{\text{Total predictions}} \times 100\%$$

A well-calibrated model should have an over-prediction rate close to 50%.

Under-prediction Rate

The percentage of times the model predicted lower than the actual sale price.

$$\text{Under-prediction Rate} = \frac{\text{Count of } \hat{y}_i < y_i}{\text{Total predictions}} \times 100\%$$

Should complement the over-prediction rate (both should sum to ~100%).

Percentile Error

Shows the range of prediction errors. For example, '90th percentile error' means 90% of predictions were more accurate than this amount.

Lower percentiles (10th, 25th) show the model's best performance, while higher percentiles (90th, 95th) show its worst cases.

Percentile % Error

Similar to percentile error but expressed as a percentage of the actual value.

Makes it easier to compare error ranges across different price levels.

Forecast Standard Deviation

A measure of how much the model's predictions typically vary from the average prediction. Lower values indicate more consistent predictions.

$$\sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (\hat{y}_i - \bar{y})^2}$$

Where ȳ is the average of all predictions.

Coefficient of Variation

A measure of prediction consistency relative to the average value. Lower values mean more consistent predictions.

$$CV = \frac{\text{Standard Deviation}}{\text{Mean}} \times 100$$

Allows comparison of variability across different price ranges.

Comparable Properties

Similar properties in the area that have recently sold, used to help estimate the value of the property.

The model analyzes these properties to understand local market conditions and pricing patterns.