Apply Data Science to the Pre-owned Auto Market - A Mercedes-Benz C-300 Case Study

Mercedes-Benz C-300 -- Model Year 2012

Car enthusiasts around the world recognize Mercedes-Benz (“MB”) as one of the best-engineered brands of all time. Its durability is unsurpassed. Its design engineering is unrivaled. Its reliability is matchless. Its road traction is legendary. Its safety is trend-setting. Consequently, its loyalty beggars description.

Though C-300 is MB’s baseline luxury model, it has the entire range of bells and whistles one expects in an upscale luxury version under $50K – from 228hp V6 to 4MATIC AWD to power sunroof to leatherette to dual climate to eight airbags to eight speakers to Bluetooth, etc., in addition to 48mo/50K bumper-to-bumper warranty.

Modeling Step 1 (Correlation Matrix)

(Click on the image to enlarge)

The above correlation matrix (1) is unrestricted, representing the entire database without any constraints whatsoever. As usual, the Dealer Price (Dealer Pr) has the highest (negative) correlation with Miles, signifying that the higher miles tend to dampen the dealers’ asking prices in the market.

Warranty is the next best predictive variable, with extremely low collinearity with the other potential independent variables. The positive coefficient points to buyer’s preference of the warranted vehicles over their counterparts with expired warranties. Unsurprisingly, Accident has a negative impact on dealer prices, while well-maintained cars (Service) are rewarded. Surprisingly, the highest-rated original ownership is unrewarded. The plausible conclusion is that the 3-yr leases are so popular in the mini world of upscale vehicles that the first owner is truly the first purchaser after the expiration of the lease.

The correlation matrix (2) is however constrained to those with the balance of the factory re-certified (Certified) warranty or special dealer warranty.  Dealer warranties are generally sales promotion measures, hence quite short-lived, often ranging between 30-day/1,000 miles and 90-day/3,000 miles, although some 1-year/limited to unlimited miles are not uncommon. While Miles and Warranty are still projecting normal relationships with the Dealer Price, Accident and Owner have switched sides. 

Given the limited period and the resulting capped mileage, the accident variable has become irrelevant (uncorrelated). On the other hand, the Owner variable has turned into a big positive now, with an equally negative relationship with Miles, suggesting that the original ownership would be rewarded as long as fewer (than normal) miles are driven. Meanwhile, Service has become the most positive correlation coefficient, emphasizing that the maintenance of the vehicle by the manual would be economically wholesome as well.

The above scatter graph depicts the usual negative relationship between the Dealer Prices and Miles. Prices generally decrease commensurately with the increasing mileage. Thus far, this graph has demonstrated the most classic relationship; nonetheless, this fit would be much tighter with the trimming of some outliers, thus paving the way for a much higher R-square, perhaps to a more customary level. 

Modeling Step 2 (Multiple Regression Analysis)

The model R-square – 0.9681076 – is reasonably high, with potential for even higher R-square if the model is rerun without the outliers.

The above MRA output confirms the negative contributory relationship between Miles and the dependent variable, meaning higher miles are negatively contributing to the predicted prices. Though the Miles coefficient is seemingly small, it will nonetheless have reasonable impact on cars with high mileage; for example, the predicted price of a 2012 C-300 with 100,000 miles will be reduced by -$2,238 (-0.022380 * 100,000), as opposed to a mere -$45 for a competing one with only 20,000 miles on it.

Accident is the most important independent variable (highest t stat and lowest P-value) in the model followed by Service, Owner and Warranty. Again, the standout presence of Accident points to the fact that it provides the maximum price differentiation between the accident-free and accident-encountered groups. Simply put, the future owners of these fairly late model upscale cars are most likely risk-averse, and as a result are unwilling to pay the high market price either for the high mileage cars or those cars that have encountered major damages or accidents.

To interpret the other Model coefficients, the well-maintained cars provide the necessary peace of mind for the buyers as they are willing to accept good service (service maintenance by the manual, garage kept, etc.) in lieu of the expired warranty (the original 4-year factory warranty period for these cars has in 2016). Additionally, the single ownership and Certified/Dealer warranty are greatly favored in retaining high value. Of course, higher miles and accidents have perceptibly negative impacts on predicted prices.    

Modeling Step 3 (Analysis of Model Estimates)

The above percentile graph shows that while the model estimates are significantly lower at the bottom end of the curve (up to the 25^th), they are however in tandem on the long end of the curve, though diverging at the outer end (> 90^th). The fact that the model has been predicting lower prices at the bottom end of the curve points to the above-the-market asking prices for the lower end units, perhaps those with multiple incidences – accidents on record, multiple ownership, inadequate maintenance or high mileage.

On the other hand, this additionally proves that the model estimates could help both consumers and dealers to quickly converge on the same page as these estimates are independently derived. Likewise, the private sellers can validate their subject prices before accepting the trade-in values from the dealers, considering that these are upscale vehicles and local comps could be few and far between.    

The above Warranty table shows that the dealers are over-charging by packaging vehicles with in-house (Dealer) warranties. On the contrary, they are significantly under-pricing – roughly $3,000 on average – the factory Certified vehicles. Vehicles without any warranty (None) are the least preferred, thus fetching -$2,000, either way. Interestingly, the vehicles with dealer warranty have far fewer miles than those with expired warranty.        

While the Model is confirming the dealer pricing for the fleet without any reported damages/accidents, the dealers are however way over-pricing the ones with the reported accidents. Therefore, by having the model estimates placed alongside the dealer prices, consumers could save on average $5,229 (18,449 – 13,220), a truly wow savings and a great firewall protection from dealers’ over-pricing.

The Model also proves that the one owner vehicles are expected to fetch premium prices, though the dealers are pricing the multiple ownership cars higher than the original owners’. Ironically, the 3-owner vehicles are priced the highest, roughly $2,650 above the market, while the 1-owner ones are the lowest, roughly $2,500 below the market. Again, this transposition of prices could be avoided if they were to subscribe to some legitimate model values. Moreover, by having the model estimates available side-by-side the dealer prices, dealers would protect average consumers and ease deal-making by eliminating all unnecessary price haggling back and forth.

Though the dealers are asking more or less the same price irrespective of the level of owner’s maintenance history, the Model is nevertheless urging a much higher price – in fact, over $3,000 – for the better maintained vehicles. Needless to say, absent model values alongside dealer prices, buyers would way overpay for the lesser maintained vehicles, proving the need to reinvent this industry by requiring a set of independent values to simultaneously coexist.

The above Miles table illustrates the price comparison by having miles broken down into four (equal) quartiles. While the Model is predicting very similar prices across all quartiles, dealers are asking significantly higher prices for the low mileage cars. Dealer prices in the high mileage quartile are somewhat lower than the model estimates. Unfortunately, the lure of the low mileage vehicles is forcing consumers to pay an unwarranted premium which could be avoided if the model estimates were also published alongside the dealer prices.

The Model is proving that the location arbitrage is virtually non-existent nationally, though the West Coast dealers are asking quite a bit higher prices than the national average. According to the Model, the West Coast prices are, on average, $900 above the real market. Of course, a normalized metric (Model Est/Miles) is an alternate way to standardize and evaluate this scenario.     

The above data sample demonstrates that the dealers are way over-pricing the cars with reported accidents. The Model, on the other hand, is heavily discounting those cars. The spread is widest when stacked with lack of warranty, multiple owners and less than perfect maintenance (e.g., SL # 2, 5 and 8). If the model estimates were to be placed alongside the dealer prices, buyers would immediately know the extent of the over-pricing.

When the modeling process identifies the under-priced cars, it’s pointing to some “upfront” savings for the consumers. This is an area where the dealers would be most benefited if they were to subscribe to some model estimates. The above sample shows that the dealers are generally under-pricing the accident-free vehicles, with the widest spreads attributed to those that are additionally backed by warranty, single ownership and excellent service history.

As indicated before, now and then, the dealer prices could consciously be lower to factor in some minor negatives (rarely captured in the modeling database) or to address some imminent psychological breakpoints. SL # 6 could be one such psychological case where the dealer might have consciously lowered the price (the lowest price) as the vehicle is on the verge of reaching 100K miles, a big psychological milestone.

Considering the popularity of the Mercedes-Benz C-300 series, the 2012 model has become one of the most sought after mid-size luxury late models on the market today.

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How to Develop a Pricing Model for a Late Model Vehicle - A Nissan Altima Case Study

Pricing Model for a Late Model Vehicle

-- 2014 Nissan Altima Case Study --

Altima has been Nissan’s bread and butter mid-size sedan for over a decade, competing with other popular mid-size brands like Toyota Camry, Honda Accord, Hyundai Sonata, Chevrolet Malibu, Ford Fusion, and a host of others. Nissan sold a record 335K in combined Altima brands in 2014, rising from a mere 203K at the bottom of the last recession in 2009. 

The 2014 Altima came in two primary engine configurations: 2.5L I4 16V and 3.5L V6 24V, with the SL Trim topping both lines. While the 3.5 SL represented the hallmark of luxury for Altima with V6 engine, moonroof, upgraded Bose audio, leather interior and a luxury power pack, the 2.5 complex (2.5, 2.5 S, 2.5 SV & 2.5 SL) collectively led the overall production and sales volume. Of course, the moonroof, Bose audio and leather were available as factory options for the 2.5 SL as well.

The modeling sample, therefore, comprises of the 2.5 and 3.5 SLs only.

Modeling Step 1 (Correlation Matrix)

As indicated before, the correlation matrix sets the table for modeling. As expected, the Dealer Price (abbreviated here as Dealer Pr) has the highest (negative) correlation with Miles, signifying that the higher miles generally dampen the dealers’ asking prices in the market.

Though Warranty is the next best predictive variable, it’s extremely high collinearity with Miles (-0.8792) makes it an insignificant variable, leaving the latter to solely represent the entire mile-related complex. As all warranties are primarily tied to the mileage (and secondarily to the number of years/months), their collinearity is observably inseparable. For instance, the original factory warranty covered the car bumper to bumper for 3-years/36,000 miles, Power-train warranty covered engine and transmission for 5-years/60,000 miles, and the factory Certified (for the pre-owned vehicles) warranty extended the Power-train to 7-years/100,000 miles.    

The Trim variable demonstrates the third highest predictive relationship with the dependent variable. Though Trim has a high collinearity with the Moonroof variable, the latter would still be tried in the model considering the limited pool of independent variables.

Unlike the older and mid-age models, Service history (Service) is usually an important consideration in purchasing late model vehicles as buyers are forced to pay up to 70% of the original MSRP for the well-maintained ones. Service is therefore a new variable which shows significant predictive promise, though somewhat correlated with Owner and Accident.

Accident is the other important predictive variable in the modeling queue, with low multi-collinearity, except for Service. Moonroof and the prior ownership (Owner) will be the other predictors in the MRA model. While prior ownership – particularly original ownership – is generally an important variable in predicting prices of the older and mid-age models, it is nonetheless much less significant for the late models as the vast majority of late model cars have single owners, thus making the variable more predictable and less disparate. The lack of distribution makes it significantly weaker.

The above scatter graph depicts the negative relationship between the Dealer Prices and Miles. Prices generally decrease commensurately with the increasing mileage. Of course, the fit would tighten with some outliers removed, thus paving the way for a higher R-square, perhaps up to a more customary level. 

Modeling Step 2 (Multiple Regression Analysis)

The model R-square – 0.976608347 – is reasonably high, with potential for even higher R-square if the model is rerun without the outliers.

The above MRA output confirms the negative contributory relationship between Miles and the dependent variable, meaning higher miles are negatively contributing to the predicted prices. Though the Miles coefficient is seemingly small, it will nonetheless have significant impact on cars with high mileage; for example, the predicted price of a 2014 with 70,000 miles will be reduced by -$3,221 (-0.04601892 * 70,000), as opposed to -$920 for a competing Altima with only 20,000 miles on it.

Accident, in sharp contrast to a lower correlation coefficient, stands out as the most important independent variable (highest t stat and lowest P-value) in the model followed by Trim and Miles. The reason Accident is so prominent in the model is that it provides the maximum price differentiation between the two groups of cars – accident-free vs. accident-encountered. Simply put, the future owners of near new cars are mostly risk-averse, negotiating significantly lower (discounted) prices for the cars that have encountered damages and accidents. Accidents, often resulting in physical damages, are not covered by the factory warranty which covers manufacturing faults only.

To interpret the other MRA model coefficients, the higher Trim model – 3.5 SL – is contributing more to the model estimate than the lower 2.5 SL Trim. Additionally, single ownership (Owner) and better serviced vehicles (Service) are preferred while Moonroof adds to the model estimate as well. Again, higher miles and accidents have recognizably negative impacts on model estimates.    

Modeling Step 3 (Analysis of Model Estimates)

The above percentile graph shows that the model estimates are significantly lower at the bottom end of the curve, zigzagging between the 25^th and 50^th percentile, and are confirming the dealer prices on the long end of the curve. The fact that the model has been predicting lower prices at the bottom end of the curve points to the above-the-market asking prices for the lower end units, perhaps those with accidents on record. On the other hand, this additionally proves that the model estimates could help both consumers and dealers to quickly converge on the same page as these estimates are independently derived. Likewise, the private sellers can validate their subject prices before accepting the trade-in values from the dealers.  

The model is predicting even higher (than the dealer) prices for the top-of-the-line 3.5 SL Trim, signifying that the market is ready to withstand higher prices for the more robust V6 engine with factory-installed power and cosmetic upgrades, even though the manufacturer sells a disproportionately higher volume of the lighter 2.5 SL version (assuming, of course, that the 2.5 SL’s 63% presence in this sample represents the actual rollout too). While the dealers are under-pricing the high-end low-volume 3.5 SLs, the model estimates are signaling the possible over-pricing of the 2.5 SLs.

The original average MSRPs for these two models were $27,920 and $30,820, respectively, pointing to ironic 56% and 49% decays in respective values.

Considering these are the late model cars without any significant exposure, the cars with reported damages/accidents comprise a low 13%.  While the Model is agreeing with the dealer pricing for the vehicles without any reported damages/accidents, the dealers are however way over-pricing their fleet of Altimas with the reported damages/accidents. Therefore, by having the model estimates placed alongside the dealer prices, consumers can save on average $4,549 (15,029 – 10,480), a truly wow savings and a great firewall protection from dealers’ over-pricing.

The major car rental companies usually start withdrawing their fleets as they approach 2 years and/or 30-40K miles, to avoid having to deal with questionable rentals. As of this writing (6/2017), only one major rental company had the 2014 inventory on sale (while others have been selling 2015 and 16) which is reflected in the sample. The above graphic shows the rental car sales are more aggressively priced than the competing dealer inventories. Even the model is showing an average savings of $1,500. Knowledgeable consumers are generally aware of this potential savings and use them as direct comps while negotiating with the dealers. Again, having the model estimates available side-by-side the dealer prices would protect average consumers and ease deal-making by eliminating all unnecessary price haggling back and forth.

The presage by the correlation matrix that a better serviced car is more likely to fetch a higher price is now emphatically confirmed by the model. The lesser maintained cars fetch bottom of the barrel prices. Of course, those cars tend to have higher miles (as shown above), disproportionately more accidents, lower order trims and sometimes multiple owners even during this short stint.

The above Miles table shows the price comparison by having miles broken down into two (equal) halves. Ceteris paribus, the lower mileage group is slightly over-priced, while the higher mileage group is appropriately priced. The lure of very low mileage vehicles (not shown here) is forcing consumers to pay an unwarranted premium which could be avoided if the model estimates were also published alongside the dealer prices.

The above table proves that the location arbitrage is virtually non-existent nationally, other than the fact that the West Coast market, though inadequately represented, is seriously overpriced. Of course, considering that West Coast is not the typical Altima country, this price imbalance could be temporary, resulting from (temporary) shortage of supplies.

The above graphic is suggesting why the Moonroof is such a highly sought after option. While it is standard in 3.5 SL sedans, it is an option for 2.5 SLs – needless to say, a worthwhile option indeed. The Model is predicting $3,000 lower value for the vehicles that are unequipped with Moonroofs.   

When the Model identifies the over-priced vehicles, it’s pointing to a silver-lining, uncovering “potential” savings. If the model estimates were to be reported alongside the dealer prices, buyers would immediately know the extent of those potential savings. The above data sample demonstrates that the dealers are way over-pricing the accident-free 2.5 SLs that are still under Full (3-year/36K miles bumper-to-bumper) factory warranty (e.g., SL # 1, 3, 7 and 9), followed by the factory Certified (7-year/100K Powertrain) units (e.g., SL # 8 and 10).

Alternatively, when the modeling process identifies the under-priced cars, it’s pointing to some “upfront” savings for the consumers. This is an area where dealers would be most benefitted if they were to subscribe to the model estimates. The above sample shows that the dealers are generally under-pricing the good (accident-free and under warranty) 3.5 SLs. Again, the above under-priced sample proves the accuracy of the model. As indicated in the previous chapter, now and then, the dealer prices could consciously be lower to factor in some minor negatives (not captured in the modeling database) or to address some imminent psychological breakpoints. SL # 8 could be one such psychological case where the dealer might have consciously lowered the price as the vehicle is on the verge of running out of the 60K Powertrain warranty.

Considering the ever-escalating popularity of the Nissan Altima brand, the 2014 model has been one of the most sought after mid-size late models on the market today.

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