We chose acoustic guitars as the research object and focused on the auction market of used goods. The AucFan media service, which enables the comparison, search, and analysis of products and price information, was used with permission from the platform owner. AucFan allows users to search for data related to product transactions on Yahoo Auctions, the largest Internet auction platform in Japan. Therefore, this service is suitable for this study, which focuses on the persistence of product prices [31].
The research indicates that Fender, Martin, Taylor, Ibanez, and Yamaha are the most prominent acoustic brands [32]. However, this study considers only two of them, MartinFootnote 1 and Yamaha,Footnote 2 because AucFan has abundant data on them. We considered these to be the representative brands in the Japanese acoustic guitar market. Although both Martin and Yamaha are well-known acoustic guitar brands, we regard them as different: Martin is a luxury brand, whereas Yamaha is a mass-market brand. Martin’s price is high [33], and Yamaha believes in the importance of producing advanced high-quality equipment at a reasonable and affordable price [34]. Therefore, by analyzing these two brands, we can also analyze the different markets in the acoustic guitar industry. Figures 1 and 2 show examples of Martin and Yamaha guitars, respectively.
Example of a Martin guitar (D-28,146 samples in analysis). Photograph taken with permission of store staff
Example of Yamaha guitar (FG-122, 5 samples in analysis). Photograph taken with permission of store staff
Different parts of the guitar have different effects on tone, so different species of wood are needed for each part. For example, the wood used in fingerboards is generally more expensive. Therefore, this study analyzed the combination of parts, wood species, and wood attributes. We used two analyses to verify the effects of wood attributes on price persistence. One analysis directly used the combination of guitar and wood species as explanatory variables to identify the wood species and specific attributes that had a significant impact on price persistence. Another analysis used a combination of guitar and wood attributes as explanatory variables to determine which attribute played a role in price persistence.
Analysis 1 used a combination of wood species and guitar parts as the explanatory variables. Because each brand uses a different species of wood, we analyzed the two brands in the first analysis. In this study, the guitar parts consist of “fingerboard,” “neck,” “top,” and “side back” (as shown in Fig. 3). In our data set, the wood used for sides and backs was the same for most guitars. Therefore, this study set the variable as “side back,” instead of separating them. This analysis determined the wood species and their specific attributes that have a significant effect on price persistence. However, we could not determine which attribute played a role in price persistence in Analysis 1. Therefore, to observe the effects of the attributes individually, Analysis 2 used the combination of the guitar part and wood attributes (i.e., traditionality, aesthetics, scarcity, and decay resistance) as the descriptive variables. As with Analysis 1, we analyzed the data for the two brands. In addition, we set the explanatory and control variables as dummy variables. Additional explanations are provided in Sects. “Explanatory variables” and “Control variables“.
Parts of acoustic guitars. Figure created by the authors. In our data set, the wood used for the sides and backs was the same for all guitars. Therefore, this study set the variable as “side back” instead of separating them
We conducted multiple regression analysis using the R programming language. The stepwise method was used to test for more appropriate models that could estimate the dependent variable. We used bidirectional elimination, because it combines the advantages of the forward selection and backward elimination methods. We input or removed variables by selecting the smallest AIC statistic. Bidirectional elimination started with no predictors, and then we sequentially added the predictors that contributed the most. After each new variable was added, any variables that no longer provided an improvement in the model fit were removed.
Sample collection
We collected product data for 2000 transactions containing product models and winning bid prices from Aucfan (1000 transactions each for Yamaha and Martin). The data acquisition period for the 1000 Yamaha samples spanned from May 1, 2021, to August 15, 2021. The Martin sample in Aucfan is smaller than Yamaha’s; therefore, the data acquisition period for the 1000 Martin samples spanned from August 17, 2020, to May 1, 2021. Only used goods were included in the analysis. Aucfan provided information on whether a product was new. After collecting the 2000 transactions, we collected more information, including on the wood species used for each part of the guitar model, the age of the guitar model, and whether the wood was natural, for each guitar. We confirmed the Yamaha old model data from the list provided by the website (this list is the official one provided by Yamaha) [36]. In addition, some sample data were not provided in the list; hence, we confirmed this information using Yamaha’s official website and the Yamaha guitar product manual [37–40]. We confirmed that the Martin guitar data mainly relied on official websites and Martin product manuals provided by other websites [41–43]. We also collected data on the characteristics of wood attributes. The criteria for organizing the attribute-specific characteristics of wood are as follows. First, dark color was determined by referring to the Wood Database [44] and Wood Museum [45]. The wood used for acoustic guitar color can be divided into (1) black, (2) brown, (3) white, and (4) yellow. Here, we considered black and brown as “dark” colors and white and yellow as “bright” colors. The decision regarding traditionality was made by considering Bennett’s wood arrangement, in which he identified the main species of traditional wood used to make guitars [5]. Third, decay resistance was determined based on the description of decay resistance in the Wood database [44]. “Durable” to “very durable” was considered satisfactory, and decay resistance was regarded as unsatisfactory. For the last item, scarcity, we also referred to the Wood Database [44] and determined that the wood included in the International Union for Conservation of Nature (IUCN) was scarce and that the wood excluded from the IUCN was not scarce [36].
We removed inadequate samples using the following process. First, we confirmed that some samples showed winning bid prices that were either too high or too low. We removed these samples, because such outliers could have produced a non-negligible bias in the analysis. (This procedure is explained in “Dependent variables” below.) Second, as mentioned, because the species of wood used for the side and back are almost the same, we set the variable as “side back” instead of separating them. However, the Yamaha sample included a few cases in which different woods were used for the back and side; therefore, we removed such data to eliminate potential bias in the analysis. Fourteen samples were removed from the Yamaha data set. Third, we removed colored guitar samples, because some guitars were painted, which would interfere with the observation of aesthetic characteristics. After we removed these unsuitable observations, the sample quantity was reduced from 1000 to 779 for Martin and 949 for Yamaha.
Dependent variables
Owing to the large differences between the winning bid prices, we converted the prices to natural logarithms for analysis. After taking the natural logarithm, we used the three-sigma rule to remove outliers [46].
After removing the outliers, we found that the data contained samples with the same model number but different winning bid prices, which may have caused bias in the analysis results. Therefore, we took the average of the winning bid price (calculated after the natural logarithmic transformation of the winning bid price) for the same guitar model and aggregated the data of the same model numbers. We used 188 samples of data for Yamaha and 159 samples of data for Martin. In the analysis, we set the dependent variables as “({y}_{mathrm{Price,Persistence}}).” In addition, the models had different numbers of samples. In the Martin data, the maximum number of samples for the same model was 146, with a minimum of two, a mean of 11, and a median of five. In the Yamaha data, the maximum number of samples was 41, the minimum was two, the mean was seven, and the median was four.
Explanatory variables
In Analysis 1, the explanatory variables were the combination of wood species and guitar parts. The explanatory variable was the wood species used in the guitar. Specifically, the species of wood used in each guitar part— fingerboard, neck, top, and side back—was set as 1 if that wood was employed in that part of the guitar and 0 otherwise. As explained above, we removed the samples from different wood species. We collected 21 combinations from Martin and 25 combinations from Yamaha as the explanatory variables. The number of explanatory variables differed between the two brands, because different wood species were used. Details on the wood used and information on its attributes are provided in Tables 1 and 2. Table 1 summarizes the wood species used for each part of the guitar for both Martin and Yamaha. Four attributes corresponding to the hypotheses were defined for each species. Table 2 shows the correspondence between the characteristics of each wood sample and the attributes discussed in the hypothesis section. For the Martin sample, we set these 21 explanatory variables as follows: “({x}_{mathrm{Fingerboard}-mathrm{Rosewood}}),” “({x}_{mathrm{Fingerboard}-mathrm{Ebony}}),” “({x}_{mathrm{Fingerboard}-mathrm{Rich lite}}),” “({x}_{mathrm{Fingerboard}-mathrm{Morado}}),” “({x}_{mathrm{Fingerboard}-mathrm{Select Hardwood}}),” “({x}_{mathrm{Fingerboard}-mathrm{Katalox}}),” “({x}_{mathrm{Fingerboard}-mathrm{Black Micarta}}),” “({x}_{mathrm{Neck}-mathrm{Mahogany}}),” “({x}_{mathrm{Neck}-mathrm{Select Hardwood}}),” “({x}_{mathrm{Neck}-mathrm{Strata bond}}),” “({x}_{mathrm{Neck}-mathrm{Spanish cedar}}),” “({x}_{mathrm{Top}-mathrm{Sitka spruce}}),” “({x}_{mathrm{Top}-mathrm{Sapele}}),” “({x}_{mathrm{Top}-mathrm{HPL}}),” “({x}_{mathrm{Top}-mathrm{Mahogany}}),” “({x}_{mathrm{Side back}-mathrm{Mahogany}}),” “({x}_{mathrm{Side back}-mathrm{Rosewood}}),” “({x}_{mathrm{Side back}-mathrm{Sapele}}),” “({x}_{mathrm{Side back}-mathrm{HPL}}),” “({x}_{mathrm{Side back}-mathrm{Koa}}),” “({x}_{mathrm{Side back}-mathrm{Siris}}).” In Yamaha, we named these 25 explanatory variables as, “({x}_{mathrm{Fingerboard}-mathrm{Rosewood}}),” “({x}_{mathrm{Fingerboard}-mathrm{Ebony}}),” “({x}_{mathrm{Fingerboard}-mathrm{Palisander}}),” “({x}_{mathrm{Fingerboard}-mathrm{Bubinga}}),” “({x}_{mathrm{Fingerboard}-mathrm{Ovangkol}}),” “({x}_{mathrm{Neck}-mathrm{Mahogany}}),” “({x}_{mathrm{Neck}-mathrm{Nato}}),” “({x}_{mathrm{Neck}-mathrm{Maple}}),” “({x}_{mathrm{Neck}-mathrm{Rosewood}}),” “({x}_{mathrm{Top}-mathrm{Spruce}}),” “({x}_{mathrm{Top}-mathrm{Yezo Spruce}}),” “({x}_{mathrm{Top}-mathrm{Palisander}}),” “({x}_{mathrm{Side back}-mathrm{Toog}}),” “({x}_{mathrm{Side back}-mathrm{Nato}}),” “({x}_{mathrm{Side back}-mathrm{Mahogany}}),” “({x}_{mathrm{Side back}-mathrm{Palisander}}),” “({x}_{mathrm{Side back}-mathrm{Rosewood}}),” “({x}_{mathrm{Side back}-mathrm{Meranti}}),” “({x}_{mathrm{Side back}-mathrm{Clantus}}),” “({x}_{mathrm{Side back}-mathrm{Walnut}}),” “({x}_{mathrm{Side back}-mathrm{Maple}}),” “({x}_{mathrm{Side back}-mathrm{Agathis}}),” “({x}_{mathrm{Side back}-mathrm{Sapele}}),” “({x}_{mathrm{Side back}-mathrm{Ovangkol}}),” “({x}_{mathrm{Side back}-mathrm{Jacaranda}}).”
In the Martin sample, multicollinearity occurred in Fingerboard-Richlite, Fingerboard-Ebony, and Fingerboard-Rosewood. Among these three variables, Fingerboard-Richlite is a synthetic material that meets only two attributes, and is thus less important. Therefore, we removed this information. In the Yamaha sample, we removed four variables because of multicollinearity. Fingerboard-Ovangkol was highly correlated with all of the fingerboard variables, and the number of samples was small; therefore, it was removed. Nato was viewed as a substitute wood for Mahogany; therefore, Neck-Nato and Side Back-Nato were removed when multicollinearity was generated.
In the analysis, we identified and interpreted wood as statistically significant for the winning bid price.
In Analysis 2, the explanatory variables were a combination of wood attributes and guitar parts. Analysis 2 used a combination of guitar and wood attributes as explanatory variables to determine which attribute played a role in price persistence. In Analysis 2, we identified whether each wood species conformed to the attribute and labelled it as “1” for conformity and “0” for non-conformity. For example, if a sample’s fingerboard used rosewood, we could check the attributes of rosewood shown in Table 2. We could then determine that rosewood matched all the four attributes, so this sample’s Fingerboard-Dark, Fingerboard-Traditionality, Fingerboard-Decay resistant, and Fingerboard-Scarcity are all scored 1. We then set the explanatory variables directly for the wood attributes and guitar parts [47]. In Analysis 2, we set 16 explanatory variables (i.e., “({x}_{mathrm{Fingerboard}-mathrm{Dark}}),” “({x}_{mathrm{Fingerboard}-mathrm{Traditionality}}),” “({x}_{mathrm{Fingerboard}-mathrm{Decay resistant}}),” “({x}_{mathrm{Fingerboard}-mathrm{Scarcity}}),” “({x}_{mathrm{Neck}-mathrm{Dark}}),” “({x}_{mathrm{Neck}-mathrm{Traditionality}}),” “({x}_{mathrm{Neck}-mathrm{Decay resistant}}),” “({x}_{mathrm{Neck}-mathrm{Scarcity}}),” “({x}_{mathrm{Top}-mathrm{Dark}}),” “({x}_{mathrm{Top}-mathrm{Traditionality}}),” “({x}_{mathrm{Top}-mathrm{Decay resistant}}),” “({x}_{mathrm{Top}-mathrm{Scarcity}}),” “({x}_{mathrm{Side back}-mathrm{Dark}}),” “({x}_{mathrm{Side back}-mathrm{Traditionality}}),” “({x}_{mathrm{Side back}-mathrm{Decay resistant}}),” “({x}_{mathrm{Side back}-mathrm{Scarcity}})”).
For Martin, more woods satisfy decay resistance, because decay resistance and dark are multicollinearity-generated in parts of the fingerboard, neck, and top. Thus, we removed decay resistance to observe the difference in the dark, meaning that fingerboard-decay resistant, neck-decay resistant, and top-decay resistant were removed. Top-Scarcity and Top-Traditionality have a strong correlation. Therefore, we removed Top-Scarcity. In addition, in the neck part, any two of Neck-Dark, Neck-Traditionality, and Neck-Scarcity will produce multicollinearity, so we are left with only one variable observation. The attribute analysis was divided according to the properties of wood. Four types of wood are used by Yamaha for the neck. The other attributes of these four types are similar, and only their scarcity is different. Two kinds of wood are scarce, and two are not; thus, we retained Neck-Scarcity.
In the Yamaha sample, we removed five variables because of multicollinearity. We also found that, in all of the parts, dark and decay resistance have a strong correlation, and more wood satisfies decay resistance; therefore, we removed decay resistance in three parts (fingerboard, neck, top), which means that fingerboard-decay resistance, neck-decay resistance, and top-decay resistance were removed, leaving the decay resistance observed in the side back part. Therefore, we removed the dark back side. In addition, traditionality and scarcity were highly correlated in the neck and top parts; therefore, as with the Martin sample, we retained traditionality to be observed in the top part and removed Neck-Scarcity and Top-Scarcity.
Control variables
First, we controlled for the effect of the age of the acoustic guitar, calculated from the year in which it was initially released. Given that the price persistence of a product may be affected by age, we analyzed the age of the acoustic guitar as a control variable. Age was measured from the 1920s to the 2020s in decadal units and was set to “1” if the year the product was first released fell into this category and “0” if it did not [47]. We named these 10 variables “({x}_{1920mathrm{s}}),” “({x}_{1930mathrm{s}})” “({x}_{1940mathrm{s}}),” “({x}_{1950mathrm{s}}),” “({x}_{1960mathrm{s}}),” “({x}_{1970mathrm{s}})” “({x}_{1980mathrm{s}}),” “({x}_{1990mathrm{s}}),” “({x}_{2000mathrm{s}}),” “({x}_{2010mathrm{s}}),” and “({x}_{2020mathrm{s}}).”
Second, we controlled for the influence of natural and artificial woods. The wood used in guitars can be divided into two types: solid and plywood. Solid wood is natural wood, whereas plywood is synthetic wood. Artificial synthetic materials are cheaper and more resistant to decay than are natural materials; however, consumers often prefer their general value [22]. Natural wood products are considered more stable, rot-resistant, natural, modern, and luxurious than laminates [48]. Therefore, naturalness (solid) was analyzed as a control variable, because product value can be affected by the naturalness of wood. Specifically, the value was set to “1” if the product was natural wood and “0” otherwise. This control variable can be used for both the top and side backs. We set these variables as “({x}_{mathrm{Solid}-mathrm{Top}})” and “({x}_{mathrm{Solid}-mathrm{Sideback}}).” However, the control variable for the side back had a high correlation with its explanatory variables, causing a multicollinearity problem. Therefore, only the top portion was included in this analysis.
Empirical specifications
We regarded a p value less than 0.05 (typically ≤ 0.05) as statistically significant. We used this criterion to identify the significant variables. We provide confirmation results for any statistical problems in the four models as follows. In Analysis 1, Martin’s mean variance inflation factor (VIF) was 1.64, and the maximum VIF was 2.48; Yamaha’s mean VIF was 1.87, and the maximum VIF was 4.33. In Analysis 2, Martin’s mean VIF was 1.35, and the maximum VIF was 2.26; Yamaha’s mean VIF was 1.51, and the maximum VIF was 2.19. We ultimately confirmed that there was no multicollinearity problem, as they were all below 5 (as a rule of thumb, VIF values above 5 or 10 indicate multicollinearity [49]).
To verify the presence or absence of heteroskedasticity, the Breusch–Pagan test was conducted. In Analysis 1, Martin’s p value in the Bruch–Pagan test was 0.04, and Yamaha’s p value in the Bruch–Pagan test was 0.02. In Analysis 2, Martin’s p value in the Bruch–Pagan test was 0.07, and Yamaha’s p value was 0.006. The Bruch–Pagan test result was typically > 0.05; hence, we used the Newey–West test to provide an estimate of the covariance matrix of the parameters of a regression-type model, except for Martin in Analysis 2.
The complete model of the four models is as follows: where β is the coefficient of each variable, C is a constant, and ε is an error term.
Model 1: Analysis 1 (the explanatory variables were the combination of wood species and guitar part [Martin])
$${y}_{rm Price}^{rm Martin1}={beta }_{1}{x}_{rm Fingerboard-Rosewood}^{rm Martin1} + {beta }_{2}{x}_{rm Fingerboard-Ebony}^{rm Martin1} + {beta }_{3}{x}_{rm Fingerboard-Richlite}^{rm Martin1} + {beta }_{4}{x}_{rm Fingerboard-Morado}^{rm Martin1} + {beta }_{5}{x}_{rm Fingerboard-SelectHardwood}^{rm Martin1} + {beta }_{6}{x}_{rm Fingerboard-Katalox}^{Martin1} + {beta }_{7}{x}_{rm Fingerboard-BlackMicarta}^{rm Martin1} + {beta }_{8}{x}_{rm Neck-Mahogany}^{rm Martin1} + {beta }_{9}{x}_{rm Neck-Select Hardwood}^{rm Martin1} + {beta }_{10}{x}_{rm Neck-Strata bond}^{rm Martin1} + {beta }_{11}{x}_{rm Neck-Spanish cedar}^{rm Martin1} + {beta }_{12}{x}_{rm Top-Sitka spruce}^{rm Martin1} + {beta }_{13}{x}_{rm Top-Sapele}^{rm Martin1} + {beta }_{14}{x}_{rm Top-HPL}^{rm Martin1} + {beta }_{15}{x}_{rm Top-Mahogany}^{rm Martin1} + {beta }_{16}{x}_{rm Side back-Mahogany}^{rm Martin1} + {beta }_{17}{x}_{rm Side back-Rosewood}^{rm Martin1} + {beta }_{18}{x}_{rm Side back-Sapele}^{rm Martin1} + {beta }_{19}{x}_{rm Side back-HPL}^{rm Martin1} + {beta }_{20}{x}_{rm Side back-Koa}^{rm Martin1} + {beta }_{21}{x}_{rm Side back-Siris}^{rm Martin1} + {beta }_{22}{x}_{1920s}^{rm Martin1} + {beta }_{23}{x}_{1930s}^{rm Martin1} + {beta }_{24}{x}_{1940s}^{rm Martin1} + {beta }_{25}{x}_{1950s}^{rm Martin1} + {beta }_{26}{x}_{1960s}^{rm Martin1} + {beta }_{27}{x}_{1970s}^{rm Martin1} + { beta }_{28}{x}_{1980s}^{rm Martin1} + {beta }_{29}{x}_{1990s}^{rm Martin1} + { beta }_{30}{x}_{2000s}^{rm Martin1} + { beta }_{31}{x}_{2010s}^{rm Martin1} + {beta }_{32}{x}_{2020s}^{rm Martin1} + {beta }_{33}{x}_{rm Solid-Top}^{rm Martin1} + {beta }_{34}{x}_{rm Solid-Sideback}^{rm Martin1} + C + varepsilon .$$
Model 2: Analysis 1 (the explanatory variables were the combination of wood species and guitar part [Yamaha]).
$${y}_{rm Price}^{rm Yamaha1}={beta }_{1}{x}_{rm Fingerboard-Rosewood}^{rm Yamaha1} + {beta }_{2}{x}_{rm Fingerboard-Ebony}^{rm Yamaha1} + {beta }_{3}{x}_{rm Fingerboard-Palisander}^{rm Yamaha1} + {beta }_{4}{x}_{rm Fingerboard-Bubinga}^{rm Yamaha1} + {beta }_{5}{x}_{rm Fingerboard-Ovankol}^{rm Yamaha1} + {beta }_{6}{x}_{rm Neck-Mahogany}^{rm Yamaha1} + {beta }_{7}{x}_{rm Neck-Nato}^{rm Yamaha1} + {beta }_{8}{x}_{rm Neck-Maple}^{rm Yamaha1} + {beta }_{9}{x}_{rm Neck-Rosewood}^{rm Yamaha1} + {beta }_{10}{x}_{rm Top-Spruce}^{Yamaha1} + {beta }_{11}{x}_{rm Top-Yezo Spruce}^{rm Yamaha1} + {beta }_{12}{x}_{rm Top-Palisander}^{rm Yamaha1} + {beta }_{13}{x}_{rm Side back-Toog}^{rm Yamaha1} + {beta }_{14}{x}_{rm Side back-Nato}^{rm Yamaha1} + {beta }_{15}{x}_{rm Side back-Mahogany}^{rm Yamaha1} + {beta }_{16}{x}_{rm Side back-Palisander}^{rm Yamaha1} + {beta }_{17}{x}_{rm Side back-Rosewood}^{rm Yamaha1} + {beta }_{18}{x}_{rm Side back-Meranty}^{rm Yamaha1} + {beta }_{19}{x}_{rm Side back-Clantus}^{rm Yamaha1} + {beta }_{20}{x}_{rm Side back-Walnut}^{rm Yamaha1} + {beta }_{21}{x}_{rm Side back-Maple}^{rm Yamaha1} + {beta }_{22}{x}_{rm Side back-Agathis}^{rm Yamaha1} + {beta }_{23}{x}_{rm Side back-Sapele}^{rm Yamaha1} + {beta }_{24}{x}_{rm Side back-Ovankol}^{rm Yamaha1} + {beta }_{25}{x}_{rm Side back-Jacaranda}^{rm Yamaha1} + {beta }_{26}{x}_{1970s}^{rm Yamaha1} + {beta }_{27}{x}_{1980s}^{rm Yamaha1} + {beta }_{28}{x}_{1990s}^{rm Yamaha1} + {beta }_{29}{x}_{2000s}^{rm Yamaha1} + {beta }_{30}{x}_{2010s}^{rm Yamaha1} + {beta }_{31}{x}_{rm Solid-Top}^{rm Yamaha1} + {beta }_{32}{x}_{rm Solid-Sideback}^{rm Yamaha1} + C + varepsilon.$$
Model 3: Analysis 2 (The explanatory variables were a combination of wood attributes and guitar part [Martin])
$${y}_{rm Price}^{rm Martin2}={beta }_{1} {x}_{rm Fingerboard-Dark}^{rm Martin2} + {beta }_{2}{x}_{rm Fingerboard-Traditionality}^{rm Martin2} +{beta }_{3}{x}_{rm Fingerboard-Decay resistant}^{rm Martin2} + {beta }_{4}{x}_{rm Fingerboard-Scarcity}^{rm Martin2} + {beta }_{5}{x}_{rm Neck-Dark}^{rm Martin2} + {beta }_{6}{x}_{rm Neck-Traditionality}^{rm Martin2} + {beta }_{7}{x}_{rm Neck-Decay resistant}^{Martin2} + {beta }_{8}{x}_{Neck-Scarcity}^{Martin2} + {beta }_{9}{x}_{Top-Dark}^{Martin2} + {beta }_{10}{x}_{Top-Traditionality}^{rm Martin2} + {beta }_{11}{x}_{rm Top-Decay resistant}^{rm Martin2} + {beta }_{12}{x}_{rm Top-Scarcity}^{rm Martin2} + {beta }_{13}{x}_{rm Side back-Dark}^{rm Martin2} + {beta }_{14}{x}_{rm Side back-Traditionality}^{rm Martin2} + {beta }_{15}{x}_{rm Side back-Decay resistant}^{rm Martin2} + {beta }_{16}{x}_{rm Side back-Scarcity}^{rm Martin2} + {beta }_{17}{x}_{1920s}^{rm Martin2} + {beta }_{18}{x}_{1930s}^{rm Martin2} + {beta }_{19}{x}_{1940s}^{rm Martin2} + {beta }_{20}{x}_{1950s}^{rm Martin2} + {beta }_{21}{x}_{1960s}^{rm Martin2} + {beta }_{22}{x}_{1970s}^{rm Martin2} + {beta }_{23}{x}_{1980s}^{rm Martin2} + {beta }_{24}{x}_{1990s}^{rm Martin2} + {beta }_{25}{x}_{2000s}^{rm Martin2} + {beta }_{26}{x}_{2010s}^{rm Martin2} + {beta }_{27}{x}_{2020s}^{rm Martin2} + {beta }_{28}{x}_{rm Solid-Top}^{rm Martin2} + {beta }_{29}{x}_{rm Solid-Sideback}^{rm Martin2} + C + varepsilon .$$
Model 4: Analysis 2 (The explanatory variables were a combination of wood attributes and guitar part [Yamaha]).
$${y}_{rm Price}^{rm Yamaha2}={beta }_{1}{x}_{rm Fingerboard-Dark}^{rm Yamaha2}+{beta }_{2}{x}_{rm Fingerboard-Traditionality}^{rm Yamaha2}+{beta }_{3}{x}_{rm Fingerboard-Decay resistant}^{rm Yamaha2}+{beta }_{4}{x}_{rm Fingerboard-Scarcity}^{rm Yamaha2}+{beta }_{5}{x}_{rm Neck-Dark}^{rm Yamaha2}+{beta }_{6}{x}_{rm Neck-Traditionality}^{rm Yamaha2}+{beta }_{7}{x}_{rm Neck-Decay resistant}^{rm Yamaha2}+{beta }_{8}{x}_{rm Neck-Scarcity}^{rm Yamaha2}+{beta }_{9}{x}_{rm Top-Dark}^{rm Yamaha2}+{beta }_{10}{x}_{rm Top-Traditionality}^{rm Yamaha2}+{beta }_{11}{x}_{rm Top-Decay resistant}^{rm Yamaha2}+{beta }_{12}{x}_{rm Top-Scarcity}^{rm Yamaha2}+{beta }_{13}{x}_{rm Side back-Dark}^{rm Yamaha2}+{beta }_{14}{x}_{rm Side back-Traditionality}^{rm Yamaha2}+{beta }_{15}{x}_{rm Side back-Decay resistant}^{rm Yamaha2}+{beta }_{16}{x}_{rm Side back-Scarcity}^{rm Yamaha2}+{beta }_{17}{x}_{1970s}^{rm Yamaha2}+{beta }_{18}{x}_{1980s}^{rm Yamaha2}+{beta }_{19}{x}_{1990s}^{rm Yamaha2}+{beta }_{20}{x}_{2000s}^{rm Yamaha2}+{beta }_{21}{x}_{2010s}^{rm Yamaha2}+{beta }_{22}{x}_{rm Solid-Top}^{rm Yamaha2}+{beta }_{23}{x}_{rm Solid-Sideback}^{rm Yamaha2}+C+varepsilon$$
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