# Empirical Evidences for Urban Influences on Public Health in Hamburg
## Materials and Methods
### Methods and Statistical Tests  
SPSS 24 was used for all statistical analyses. The total number of variables used for the principal component analysis (PCA) is 41, representing the survey questions described in Section 2.1, which could be included in the analyses according to their type of question or answer scale. We chose an explorative PCA for two reasons. The primary purpose was to test the conceptual systematization of the UrbWelth model. Secondly, all variables connected to the subjective rating of health were to be identified, guiding the selection of independent variables for the linear regression model (LR), which is our second main analysis method (see Section 3.2). All variables of the principal component \"health\" (including SRH) were excluded from the list of independent variables in the LR. Subsequently a LR was conducted to identify the most important variables that impact SRH and to model the respective influence of each of these variables. There are some general requirements that should be met for a PCA. Firstly, the relationship between the variables should be linear. Secondly, the certainty of the results depends on the sample size [90]. Both these criteria are met by our data (see Section 3.1). Thirdly, the variables should be continuous, although ordinal data are often used [91]. Lastly, there should be no outliers in the data. These last two criteria are only partly fulfilled by our data. We have countered this by excluding individual variables that did not match these requirements. Table 1 gives an overview of the variables used. The first column provides a number, used as an ID; the second column shows the content of the questions. The third column introduces abbreviations which will be used throughout the paper when referring to specific variables. Column four provides the number of valid cases (\(N\)) ranging from 953 to 1077, followed by Mean, Min, Max, and standard deviation (SD). Additional information on the type of answer scale and the answering options available is given in column five, comprising different numbered types. The main prerequisite for the multiple LR is that the data exist on an ordinal scale that is also considered an interval scale (assumption: equal distances between the classes). Further requirements \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**No.** & **Question** & **Variable** & \(n\) &
\begin{tabular}{c} **Scale** \\ **Type** \\ \end{tabular} & **Mean** & **Min** & **Max** & **SD** \\ \hline
35. & Gender & GEN & 1073 & 7 & - & - & - & - \\ \hline
36. & Daily fruit consumption & DFC & 1047 & 8 & 1.85 & 0 & 7.5 & 1.03 \\ \hline
37. &
\begin{tabular}{c} Frequency of alcohol \\ consumption \\ \end{tabular} & FAC & 1052 & 6 & 3.15 & 1 & 6 & 1.35 \\ \hline
38. & Smoking & SMO & 1044 & 5 & 2.73 & 1 & 4 & 1.14 \\ \hline
39. &
\begin{tabular}{c} Highest level of education \\ reached \\ \end{tabular} & EDU & 1056 & 9 & 6.31 & 1 & 9 & 2.61 \\ \hline
40. &
\begin{tabular}{c} Approximate monthly net \\ income of household \\ \end{tabular} & INC & 953 & 10 & 5.74 & 1 & 11 & 2.73 \\ \hline
41. & Age & AGE & 1048 & 8 & 51.86 & 18 & 95 & 18.69 \\ \hline \hline \end{tabular}  
* Scale Types: 1 = Five-levels (no, little, moderate, severe, extreme); 2 = Six-level Likert (very satisfied, satisfied, rather satisfied, dissatisfied); 3 = scale from 0 (worst health you can imagine) to 100 (best health you can imagine); 4 = Six-level Likert (very good, good, rather good, rather bad, bad, very bad); 5 = Four-level Likert (very much, quite, some-what, not at all); 6 = Six frequency levels; 7 = three categories (incl. other); 8 = open; 9 = nine categories; 10 = eleven classes in 500 \(\xi\) steps; without limit from 5000 \(\xi\) up.  
\end{table} 
Table 1: _Cont._are a linear relationship between the variables, no outliers in the data, independence of the error terms, a check for multicollinearity, and homoscedasticity and a normal distribution of the residuals.