The Art of Encoding Categorical Variables in an Automated Valuation Model (AVM)

Target Audience: New Graduates/Analysts

Dummy Coding, Effects Coding, and One-Hot Coding

Dummy encoding is used to avoid perfect multicollinearity in a regression model, a phenomenon also known as the dummy variable trap. This occurs when one dummy variable can be perfectly predicted from the others. For example, if you have three dummy variables for Town A, Town B, and Town C, the variable for Town D can be inferred when all three are 0. This can lead to issues in estimating the model coefficients. Dummy encoding handles this by using one fewer dummy variable than the total number of categories, with one category serving as the baseline or reference.

Dummy coding and effects coding both use binary variables to represent categorical data in a regression model, but they differ in how they define the baseline or reference group. In dummy coding, the baseline group is represented by a set of zeros for all dummy variables. In effects coding, the baseline group is represented by a set of -1s. So you are correct.

How Dummy Coding and Effects Coding Differ

Dummy Coding

In dummy coding, if you have five towns (let's say A, B, C, D, and E), you'd create four dummy variables (Town B, Town C, Town D, and Town E) with Town A as the baseline.

·        A house in Town A would be coded as (0,0,0,0).

·        A house in Town B would be coded as (1,0,0,0).

·        A house in Town C would be coded as (0,1,0,0).

·        A house in Town D would be coded as (0,0,1,0).

·        A house in Town E would be coded as (0,0,0,1).

The coefficient for Town B would represent the difference in the dependent variable between Town B and Town A. The intercept would represent the mean of the dependent variable for the baseline group, Town A.

Effects Coding

In effects coding, with the same five towns, you would also create four dummy variables. However, the coding for the baseline group differs.

·        A house in Town A would be coded as (−1,−1,−1,−1).

·        A house in Town B would be coded as (1,0,0,0).

·        A house in Town C would be coded as (0,1,0,0).

·        A house in Town D would be coded as (0,0,1,0).

·        A house in Town E would be coded as (0,0,0,1).

In this case, the coefficient for Town B would represent the difference between the mean of Town B and the grand mean of all towns. The intercept would represent the grand mean of the dependent variable for all towns combined.

In both dummy coding and effects coding, the reference or baseline group is not directly included in the regression equation as a separate variable.

The reason is to avoid multicollinearity, a phenomenon known as the "dummy variable trap." If you were to include a variable for all five towns, the fifth variable would be perfectly predictable from the other four. For example, if a house is not in towns A, B, C, or D, it must be in town E. This perfect linear relationship between the variables makes it impossible for the regression model to uniquely estimate the coefficients for each variable.

How the Baseline is Accounted For

Even though the baseline group isn't explicitly in the equation, its information is implicitly included through the intercept and the interpretation of the other coefficients.

Note: "Effects Coding" and "Effect Coding" are often used interchangeably, and both are generally understood to refer to the same statistical method. However, "Effects Coding" is the more common and technically precise term used in academic literature and statistical software documentation.

The name "Effects Coding" is derived from the fact that it measures the "effect" of each group relative to the overall grand mean of all groups. In a balanced design (equal sample sizes in all groups), the intercept represents this grand mean. The coefficients for the dummy variables represent the deviation of each group's mean from the overall grand mean.

Key Takeaway

·        Effects Coding: This is the most widely accepted and formal name.

·        Effect Coding: While technically less common, it is also frequently used and understood in the same context.

One-hot encoding, on the other hand, creates a binary variable for each category.

To use one-hot encoding for the four towns in a regression model, you'll create four separate binary variables, one for each town. Each observation will have a 1 in the column corresponding to its town and a 0 in the other three town columns.

While this approach introduces multicollinearity if all one-hot encoded variables are included in the model along with an intercept, it can be handled in a few ways:

·        Dropping one of the one-hot encoded variables. This effectively makes the model identical to dummy coding, with the dropped variable serving as the reference category.

·        Omitting the intercept from the model. If you use all four one-hot encoded variables but remove the intercept, the model can still be estimated. In this case, each coefficient represents the average house price for that specific town. This approach is less common in standard regression analysis but is a valid alternative.

For a regression model, omitting the intercept would make the coefficients directly interpretable as the average price for each town, all else being equal. However, if you are also including other variables, such as square footage, the coefficients would represent the effect of being in that town, holding other variables constant, relative to a baseline of zero for the other towns. This interpretation can be less intuitive than the standard approach of using a reference category.

Therefore, most regression practitioners prefer to drop one dummy variable and include an intercept.

The Role of Quantitative Variables in Automated Valuation Modeling (AVM)

Target Audience: New Graduates/Analysts

In statistics, a quantitative variable is a variable that can be measured and compared in magnitude. The three main types of quantitative variables are continuous, ratio, and discrete.

Continuous variable: A continuous variable can take any numerical value within a range. For example, in an AVM, the sale price is a continuous variable because it can take on any value within a specific range, such as $100,000 or $200,000. This variable type helps measure variation and compares different values along a continuum.

Ratio variable: A ratio variable, like the adjusted sale price per square foot (SP/SF), is a powerful tool in property valuation. It has a true zero point, meaning that a value of zero indicates the absence of the measured quantity. This precision enables meaningful comparisons of ratios and proportions, enhancing the accuracy of property valuation.

Discrete variable: A discrete variable, such as the median monthly sale prices, is a versatile tool in property valuation. It takes on specific numerical values that are separate and distinct from one another, allowing for counting and representing categories or events. This versatility makes it adaptable to various property valuation scenarios.

In an AVM, using these three types of quantitative variables – sale price (continuous), SP/SF (ratio), and median monthly sale prices (discrete) – will help capture different aspects of the housing market in a specific county. By incorporating these variables, analysts can provide a more comprehensive and accurate valuation of properties based on various metrics and factors.

Continuous vs. Ratio Variable

Suppose you are developing an AVM for a specific county with arms-length sales from the recent nine quarters. Before starting the regression modeling, you must understand the nuances of the adjusted sale price in raw and normalized (SP/SF) forms. Here is how to compare and contrast their statistical measures.

1. Mean:

• Adjusted Sale Price Mean: $436,481
• SP/SF Mean: $218.99

Comparison: The mean provides the average value of the data. It is a central measure that can help understand the general value of properties in the dataset.

Contrast: While the adjusted sale price gives an overall average value for properties sold, the SP/SF mean provides a value standardized by property size. This can help in comparing properties of different sizes.

2. Standard Error:

• Adjusted Sale Price Standard Error: $1,415
• SP/SF Standard Error: $0.44

Comparison: The standard error indicates the variability or uncertainty in the mean estimate. A smaller standard error suggests a more precise estimate.

Contrast: The standard error for adjusted sale price and SP/SF helps assess the reliability of the mean estimates. Understanding the accuracy of the valuation predictions is particularly important in AVMs.

3. Median:

• Adjusted Sale Price Median: $401,962
• SP/SF Median: $214.26

Comparison: The median represents the middle value of the dataset when arranged in order. It is a robust measure that is not affected by extreme values.

Contrast: Using the median alongside the mean provides a more complete picture of the data distribution. It can help identify any skewness or outliers that may affect the valuation model.

4. Mode:

• Adjusted Sale Price Mode: $381,196
• SP/SF Mode: $194.89

Comparison: The mode is the most frequently occurring value in the dataset. Understanding common pricing trends can be useful.

Contrast: While the mean and median provide central measures, the mode offers insight into the most common price points. This information can be valuable in identifying pricing patterns and preferences in the housing market.

5. Standard Deviation:

• Adjusted Sale Price Standard Deviation: $153,531
• SP/SF Standard Deviation: $48.26

Comparison: The standard deviation measures the dispersion of the data points around the mean. A higher standard deviation indicates greater variability in the dataset.

Contrast: Understanding the standard deviation for both adjusted sale price and SP/SF helps assess the spread of property values and can aid in determining the level of risk associated with valuation estimates.

6. Kurtosis:

• Adjusted Sale Price Kurtosis: 1.02213
• SP/SF Kurtosis: 9.4649

Comparison: The kurtosis value for the adjusted sale price is around 1.02213, indicating a normal distribution with moderate tail heaviness.

Contrast: However, the SP/SF kurtosis value of 9.4649 suggests a highly peaked distribution or heavy tails, indicating a departure from normality and the potential presence of outliers or extreme values.

7. Skewness:

• Adjusted Sale Price Skewness: 1.10514
• SP/SF Skewness: 1.8910

Comparison: Both the adjusted sale price and SP/SF skewness values are positive, indicating right-skewed distributions where the tail is on the right side of the peak.

Contrast: The skewness values suggest that the data is skewed toward higher values, with the SP/SF distribution exhibiting slightly higher skewness than the adjusted sale price.

In essence, each of these statistical measures provides valuable insights into the distribution, variability, and central tendencies of the property values in the dataset. By accounting for different aspects of the data distribution, incorporating these measures in an AVM can enhance the accuracy and reliability of the valuation predictions.

Important to Understand

Analyzing the sale price per living square foot (SP/SF) as a normalized ratio can provide additional insights and a more meaningful perspective in understanding the local housing market for several reasons:

1. Standardization: SP/SF makes comparing properties of differing sizes easier. This allows for a more direct comparison (apples-to-apples) based on the property's value relative to its size.

2. Fair Comparison: SP/SF provides a fair comparison between properties of different sizes. This can help evaluate the value propositions of properties, irrespective of their size.

3. Market Analysis: SP/SF can help identify trends in pricing per unit area over time. It can reveal whether there are specific patterns in how prices change based on property size, which can be valuable for market analysis.

4. Understanding Value: Analyzing the SP/SF can provide insights into the value buyers place on living space. It can help understand preferences for larger or smaller properties and their corresponding price points.

5. Property Valuation: SP/SF is a standard metric real estate professionals use for appraisals and property valuation purposes. It allows for a standardized approach to assessing property values.

However, it's important to note that while SP/SF offers several advantages, it should not be the sole metric for analyzing the local housing market. Raw sale prices may still be relevant, especially when considering other factors such as location, amenities, market conditions, and property features. Both metrics provide valuable insights, and a comprehensive analysis should consider both normalized and raw prices to understand the local housing market.

Discrete Quantitative Variable

A discrete variable is a quantitative variable that can take on a finite number of distinct and separate values; for instance, if we have the median sale prices for each month from January to December, each month (e.g., January, February, March, etc.) represents a discrete value for the median sale price.

These values can be measured, counted, and analyzed numerically, thereby meeting the criteria for a discrete quantitative variable.

The variable doesn't exist on a continuous spectrum. There aren't "in-between" months or quarters, so one can't have a 1.3rd quarter or July and a half. There are distinct categories (months or quarters) with clear boundaries. Even though it's not continuous, the variable represents numerical values. One can order the months (1st, 2nd, 3rd...) or quarters (Q1, Q2, Q3, Q4) in a sequence.

In summary, while months and quarters are categories, they have a defined order and can be used in calculations, making them discrete quantitative variables.

Example

The breakdown of the median sale price and median SP/SF by quarter creates discrete quantitative variables. Discrete variables can take on a finite number of values within a specific range. In this case, the number of possible values for the median sale price and median SP/SF is limited by the number of quarterly sales.

Here’s an analysis of the breakdown of the two variables in the table you provided:

    1) Median Sale Price: There is a seasonal pattern to the median sale price, with higher prices in the second and third quarters (Q2 and Q3) and lower prices in the first and fourth quarters (Q1 and Q4). This could be due to several factors, such as buyer behavior or listing availability. For example, more people may be looking to buy a house in the spring and summer months, which could drive prices higher. Additionally, sellers may be more motivated to sell their homes before the end of the year, potentially leading to lower prices in Q4.

   2) Median SP/SF: The median SP/SF also shows a seasonal pattern, with higher prices in Q2 and Q3 and lower prices in Q1 and Q4. This suggests that the seasonal pattern in the median sale price is likely due to changes in the types of properties sold rather than in the county's overall housing prices. For example, a higher proportion of larger homes may be sold in Q2 and Q3, which would drive up the median SP/SF.

Overall, the breakdown of the median sale price and median SP/SF by quarter, which yields a discrete variable, can help explain seasonal trends in the housing market. This information can also help build a more accurate AVM by considering when a property is sold.

In conclusion, understanding the different types of quantitative variables empowers analysts to leverage the data effectively. Combining continuous, ratio, and discrete variables provides a comprehensive view of the housing market, making AVM a valuable tool for property valuation.

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The Art and Science of Time Adjustments in AVM – Part 2 of 2

Part 2 of 2

Time Adjustment in AVM (Quick Review):

Automated valuation models (AVMs) adjust sale prices to account for changes in market conditions between a property's sale and valuation dates. Because real estate markets fluctuate, a house sold last year may not be directly comparable to an identical house sold today. Here is why time adjustment is needed:

1. Adjusting sale prices to reflect the market conditions at the valuation date allows the model to provide a more accurate estimate of the property's value on the target valuation date. This precision, achieved through diligent time adjustments, inspires confidence in the AVM's reliability. 

2. Time-adjusted sale prices improve model accuracy by ensuring that the model considers market trends, leading to more reliable valuations. 

3. Consistent time adjustment across all comparable properties enhances model consistency, allowing the model to compare "apples to apples" when estimating the value of the subject property.

By incorporating time-adjusted sale prices as the dependent variable rather than raw sale prices in the regression-based AVM, the model can produce more realistic and reliable property valuations that reflect market conditions at the valuation date.

Using an Extended Time Series dataset

(Click on the image to enlarge)

Suppose you are developing an AVM using a single-family home sales dataset sample from a specific county, with sales from the previous nine quarters (Q1-2022 to Q1-2024). The target is to value properties on April 1, 2024. So, the regression model's dependent variable (sale price) must be adjusted to the target valuation date.

There are two common median-based methods for time-adjusting sales prices:

1) Sale price adjustment: This method adjusts the entire sales price for changes in the market over time. It calculates a percentage change in the median sale price from the sale date to the target valuation date, then applies it to individual sale prices to adjust them to the target valuation date. 

·              Advantages:

o   Easier for users of the AVM to understand and interpret.

o   Less susceptible to outliers caused by unusually large or small homes because it considers the whole property, not just the price per square foot.

Disadvantages:

o It doesn't account for size differences between houses. A few large, expensive homes in an affluent neighborhood can skew the median up, making it a less accurate reflection of the value of smaller homes.

2) SP/SF adjustment: This method adjusts the sales price per square foot (SP/SF) for changes in the market over time. It calculates a percentage change in the median SP/SF from the sale date to the target valuation date, then applies it to the individual SP/SF figures to adjust them to the target valuation date.

            Advantages:

o   Takes into account the size of the property, providing a more standardized price measure.

o   This can be particularly important in areas with a mix of large and small houses.

Disadvantages:

o   It can be more difficult for users to understand the metric's meaning, especially for recent graduates unfamiliar with real estate valuation.

o   More susceptible to outliers caused by unusually high or low prices per square foot.

Analyzing the two methods – Median Sale Price and Median Sale Price per Square Foot (SP/SF) – for adjusting the dependent variable in the AVM regression model using single-family home sales data requires a comparative evaluation based on averages, standard deviations, and coefficient of variation (CV).

1.    Median Sale Price Method:

o    Average Median Sale Price: $394,139

o    Standard Deviation of Median Sale Price: $11,567

o    Coefficient of Variation (CV) for Median Sale Price: 2.93%

2.    Median Sale Price per Square Foot (SP/SF) Method:

o    Average Median SP/SF: $210.00

o    Standard Deviation of Median SP/SF: $5.84

o    Coefficient of Variation (CV) for Median SP/SF: 2.78%

Comparative Analysis:

- The Coefficient of Variation (CV) for the Median Sale Price method is slightly higher than that for the Median SP/SF method, suggesting that the Median Sale Price has slightly higher relative variability.

- The Median Sale Price per Square Foot method could be more robust due to the lower Standard Deviation and CV, implying that the SP/SF values are less dispersed around the average than the Median Sale Price.

Considering the comparative analysis, the Median Sale Price per Square Foot (SP/SF) method may be preferable for adjusting the dependent variable in the AVM model. The lower variability and CV suggest that using SP/SF as a measure may provide more stability and consistency in estimating property values for the target month of April 2024. This method could offer more reliable and accurate valuation predictions than the Median Sale Price method.

Alternative Method – Two-quarter Moving Averages

Using a two-quarter moving average can help smooth out the quarter-to-quarter volatility in the data and potentially provide a more stable trend for analysis. It can help reduce the impact of short-term fluctuations and noise in the data, making it easier to identify underlying patterns and trends.

Calculating a moving average of the sales data over two quarters can create a more stable trend line that captures the market's medium-term changes rather than its short-term ups and downs. This can be particularly useful when the data exhibits high volatility or seasonality.

In terms of statistical significance, a moving average can help reveal longer-term patterns and trends that may not be as apparent when looking at the unadjusted quarterly medians. By smoothing the data, you can identify more meaningful relationships and patterns that are statistically significant.

However, it's essential to note that using a moving average involves a trade-off between responsiveness to changes and smoothing out volatility. A two-quarter moving average may not capture rapid market shifts as effectively as using unadjusted quarterly medians, but it can provide a more stable, easier-to-interpret trend for analysis.

Overall, using a two-quarter moving average can be a valuable approach for reducing noise and volatility in single-family home sales data and uncovering more statistically significant trends and patterns over time.

Simple Moving Average vs. Exponential Moving Average

In a two-quarter Simple Moving Average (SMA) calculation, you typically average the values of the current quarter and the previous quarter's values. This method helps smooth out data fluctuations and gives you a clearer trend over time.

To calculate a two-quarter SMA, you would sum the current quarter's and previous quarters' values and then divide by 2. This would give you the moving average for that particular quarter.

If you were to average the current quarter and the prior moving average, it would be a different type of moving average calculation known as an Exponential Moving Average (EMA), which gives more weight to recent data points.

This table shows the Simple Moving Average (SMA) and Exponential Moving Average (EMA) values calculated for the prior nine quarters from the same home sales data. To determine which method produces smoother and less volatile values that are more suitable for adjusting raw sales prices (leading to a statistically significant time-adjusted sale price), we can analyze:

1.    SMA (Simple Moving Average):

• SMA calculates the average of a given set of prices over a specific period by equally weighting each price.
• When comparing the SMA to the Median Sale Price (MSP), we find that SMA values tend to track the MSP more closely but may lag behind significant price changes.
• The percentage difference between SMA and MSP ranges from 96.06% to 102.60%, indicating some volatility in SMA values relative to MSP.
• SMA generally irons out short-term fluctuations and is suitable for identifying trends over time. However, its responsiveness to recent price changes may be slower than that of the EMA.

2.    EMA (Exponential Moving Average):

• EMA places more weight on recent prices, making it more responsive to recent price changes than SMA.
• The EMA values tend to be further from the MSP and exhibit greater volatility than the SMA. The percentage difference between EMA and MSP ranges from 94.10% to 102.29%, showing more fluctuation in EMA values.

The percentage differences between the EMA and MSP values are higher than between the SMA and MSP values. This means the EMA values exhibit more fluctuation relative to the MSP than the SMA values.

Therefore, based on this analysis, we conclude that the SMA method yields smoother, less volatile values that are better suited to adjusting raw sales prices to create a time-adjusted sale price for use as the dependent variable in a regression-based AVM in this scenario.

Monthly vs. Quarterly Adjustments (Extended Time Series)

Monthly adjustments can introduce more noise and volatility into the data, making the dependent variable less stable than quarterly adjustments. Monthly data often reflect short-term fluctuations and can be influenced by factors such as seasonality, irregular events, or other short-term variations.

This inherent noise and volatility in monthly data can make it challenging to accurately identify and interpret underlying trends. It may also lead to a less stable dependent variable when constructing AVMs, which aim to predict property values based on historical sales data.

By using quarterly adjustments instead of monthly ones, you can smooth out some short-term fluctuations and reduce the noise in the data. Quarterly adjustments provide a more aggregated and stable representation of trends over time, which can help create a more reliable and robust dependent variable for modeling purposes.

Ultimately, the choice between monthly and quarterly adjustments should be guided by the specific characteristics of the data, the objectives of the analysis, and the trade-offs between noise reduction and the capture of short-term dynamics. It's essential to carefully consider the implications of different adjustment intervals (e.g., using 3-quarter moving averages if you are using 3 years of sales) and choose the approach that best aligns with the analysis's goals.

Conclusion

This blog post illustrates the importance of time-adjusting sale prices to create a reliable and stable dependent variable for regression-based AVMs. By using sales data across multiple quarters and employing methodologies such as Quarterly Median Sale Price per Square Foot and Simple Moving Average, the benefits of smoothing volatility and creating a more consistent time-adjusted sale price variable have been demonstrated.

The examples show that the Quarterly Median Sale Price per Square Foot and the Simple Moving Average methods yield smoother, less volatile values, making them ideal choices for time adjustment in an AVM. However, it is crucial to exercise caution and ensure that the selected methodology aligns with the specific characteristics of the real estate market under analysis. This responsibility is critical to mitigating potential risks.

By incorporating these time-adjusted sale prices into the valuation process, analysts and new graduates can enhance the accuracy and reliability of their regression models, ultimately producing more robust and dependable property valuations.

Disclaimer: This blog post serves as a starting point. As you gain experience with AVMs, you can explore more advanced time-adjustment techniques and refine your model for optimal performance. Remember, continuous learning is a journey, and support and encouragement are available along the way.

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The Art and Science of Time Adjustments in AVM - Part 1 of 2

Target Audience: New Graduates/Analysts

Part 1 of 2

In Automated Valuation Models (AVMs), time adjustment is crucial for accurately assessing property values. This process involves applying quantitative adjustments to the sale prices of comparable properties to reflect their estimated value on a specific date, known as the valuation date. Time adjustments are integral to AVMs as they ensure that the estimated value of a property aligns closely with its market value at the specified valuation date. By considering the impact of time on property values, AVMs can provide more reliable, up-to-date valuations for real estate properties.

Imagine you're valuing a house in May 2024. You have data on houses with similar characteristics that sold in the previous year (2023). Without a time adjustment, the AVM would directly compare 2023 sale prices to the subject property in 2024, which wouldn't be accurate because the market might have changed between those periods.

This adjustment accounts for potential market changes and ensures that an AVM built on 2023 sale prices yields accurate results when valuing unsold properties in 2024. This meticulous approach enhances the precision and relevance of property valuations, reflecting the dynamic nature of real estate markets and providing valuable insights for industry professionals.

Example 1

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Suppose you are developing an Automated Valuation Model (AVM) for a specific county using fifteen months of single-family home sales data, from January 2023 to March 2024. The valuation date is April 1, 2024. You are conducting a regression analysis with the sale price as the dependent variable and three essential characteristics and months as independent variables. In this regression output, the "MONTHS" variable you used represents the number of months since the sale. Therefore, a sale in January 2023 will receive a value of 15 (April 2024 minus January 2023), while a sale in March 2024 will receive a value of 1. Now, applying the coefficient to months, sales for January 2023 will be increased by $18,615 ($1,240.97 multiplied by 15), and sales for March 2024 will be increased by $1,240.97 (multiplied by 1). 

Note: No additional location variable is needed, as the time adjustment must be at the county level. You aim to use this regression analysis to derive a time coefficient that will help adjust all sales to the valuation date, resulting in a time-adjusted sale price. The time-adjusted sale price will then be used as the dependent variable in the modeling dataset. The time-adjusted sale price will help standardize sales data to a common valuation date, enabling more accurate comparisons and predictions of property values.

The regression analysis helps achieve two key goals for an AVM:

1.  Derive a time coefficient: The coefficient for the MONTHS variable ($1,240.97) represents the average monthly change in sale price. You can adjust sale prices to your valuation date (April 1, 2024). For example, a sale that closed in January 2023 can be adjusted by adding 15 months * $1240.97 to the sale price.

2.  Identify other essential factors: The coefficients for the other variables (LAND AREA, LIVING AREA, BLDG AGE) indicate the impact of these characteristics on sale prices. This information can be used in the next stage of your AVM modeling process.

Overall, the regression analysis provides a statistically sound foundation for building your AVM. By incorporating the time coefficient and the identified relationships between other characteristics and sale prices, you can create a model that estimates sale prices for single-family homes in your county.

Example 2

In this example, you use 27 months of single-family home sales data from January 2022 to March 2024. The valuation date is April 1, 2024. Again, the "MONTHS" variable represents the number of months since the sale. For instance, a sale in January 2022 will receive a value of 27 (April 2024 minus January 2022), while a sale in March 2024 will receive a value of 1. For example, sales for January 2022 will be adjusted up by $12,869 ($476.62 multiplied by 27), and sales for March 2024 will be adjusted by $476.62 (multiplied by 1).

Based on this regression analysis, you have determined the coefficients for adjusting sale prices based on the number of months since the sale. This time adjustment allows you to standardize all sales to the April 1, 2024, valuation date.

To extend this analysis to the regression modeling for your AVM, you will incorporate the time-adjusted sale prices (dependent variable) into a new dataset, alongside other relevant features of the county's single-family homes. By using this adjusted sale price as the dependent variable and including other important variables (such as property characteristics, location factors, market trends, etc.) as independent variables, you can build a predictive model that estimates home values accurately for the valuation date across the county. This regression model will help you generate automated valuations for single-family homes based on their unique attributes and the time adjustment derived from the regression analysis.

Important to Note

In this case, where the intercept was forced to zero primarily to generate the time coefficient for adjusting sale prices to a standard valuation date, it can be considered statistically valid, given the specific goal of deriving time-adjusted sale prices rather than estimating the actual property values.

When moving to a regression model, it is recommended to include the intercept to achieve a more comprehensive and accurate valuation model. By capturing the overall baseline level of property values, this practice can improve your AVM's predictive ability and reliability.

Conclusion

Given the volatility in monthly time-series data, a multiple-regression-based analysis is recommended to develop smoother, more accurate time-adjustment factors for automated valuation modeling. This analysis should include a combination of time (i.e., the "Months since Sale" variable) and essential property characteristics, such as Land SF, Living SF, and Year Built. By incorporating these essential property characteristics (alongside the time variable), analysts can create a comprehensive framework that accounts for various factors influencing property values. This regression analysis yields a time coefficient that can be used to adjust the raw sale price and generate a time-adjusted sale price, which will then serve as the dependent variable in the modeling process. This two-step regression process will generate more accurate AVM values, targeting the valuation date.

Note: In part 2 of 2, we will discuss the method for handling extended time-series data. 

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