*3.3. Mathematical Approach for Data Analysis*

In general, logistic regression is a form of multiple regression with a categorical outcome variable and categorical or continuous predictor variables. In its simplest form it is possible to forecast which of two categories a person is likely to belong to given some other details [41]. In this study, the two outcome categories are represented by "Future-Refurbishers" and "Non-Refurbishers." The predictor variables, in turn, are represented by the underlying factors of the questions and statements presented in Section 3.1.

In multiple linear regression, Y is, as presented in Equation (1), predicted by a combination of predictor variables multiplied by their respective regression coefficients:

$$\mathbf{Y}\_{\text{i}} = \mathbf{b}\_{0} + \mathbf{b}\_{1}\boldsymbol{\chi}\_{1\text{i}} + \mathbf{b}\_{2}\boldsymbol{\chi}\_{2\text{i}} + \dots + \mathbf{b}\_{\text{n}}\boldsymbol{\chi}\_{\text{n}\text{i}} + \varepsilon\_{\text{i}} \tag{1}$$

Instead of predicting the value of a variable Y from several predictor variables Xn, in binary logistic regression a probability P(Y) of Y occurring given known values of Xn is determined with Equation (2):

$$P(\mathbf{Y}) = \frac{1}{\mathbf{1} + \mathbf{e}^{-(\
\mathbf{b}\_0 + \mathbf{b}\_1 \mathbf{X}\_{\text{li}} + \mathbf{b}\_2 \mathbf{X}\_{\text{2i}} + ... + \mathbf{b}\_n \mathbf{X}\_{\text{ni}} + \mathbf{e})}}\tag{2}$$

In this equation e is the base of the natural logarithm and the other coefficients form a linear combination. By expressing the multiple linear regression equation in logarithmic terms (called the logit) the results of the equation vary between 0 and 1. Thus, a value close to 1 means that Y is very likely to have occurred while a value close to 0 expresses the opposite [41]. The coefficients of the predictor variables are determined by using maximum-likelihood estimation. This estimation method selects coefficients that make the observed values most likely to have occurred [41]. Based on these values so-called "odds" and "odds ratios" (the proportionate change in odds due to a unit change in the predictor variable) can be calculated [41]. These odds ratios and the regression coefficients are presented hereinafter in Section 4.

For identifying relevant factors behind the introduced statements, we used the IBM SPSS Statistics 23 analysis program. Due to the high amount of initially considered influencing factors, a stepwise logistic regression was used for identifying the most important factors capable of distinguishing the survey participants into "Future-Refurbishers" and "Non-Refurbishers." Due to potential suppressor effects (those effects occur when a predictor has a significant effect but only when another variable is held constant) we used the stepwise backward method. In [42], this method is described as follows: "With this method, the initial model contains all of the terms as predictors. At each step, terms in the model are evaluated, and any terms that can be removed without significantly detracting from the model are removed. In addition, previously removed terms are reevaluated to determine if the best of those terms adds significantly to the predictive power of the model. If so, it is added back into the model. When no more terms can be removed without significantly detracting from the model, and no more terms can be added to improve the model, the final model is generated." The thresholds for this procedure were PIN = 0.05 and POUT= 0.10. The stepwise backward method was used in order to reduce the risk of a Type II error (i.e., missing a predictor that does in fact predict the outcome) which would be more likely with the alternative method of stepwise forward selection [41]. This method in essence follows an opposite procedure than the stepwise backward method but starts with no model terms (except the constant) in the equation. The third general method available in SPSS when conducting a binomial logistic regression is the default mode called 'enter'. This method simply adds all terms into the equation [42].
