## 4 Study Results
### Direction and Strength of Biases
As a result, explanatory variables in the first two principal components of PCA cumulatively account for 34% of the variation in our data set (Table 5). This result proves that reducing dimensions in this dataset is a challenging, due to a relatively low information overlap among analysed variables. In this two-dimensional PCA, the hot hand fallacy, together with availability and confirmation, seem to be the variables that explain the most variance. At the same time, the amount of investment is the least important variable (see Figure 3). Those factors also had a higher range of variation among investors, which therefore explains the greater degree of dispersion observed than with the other biases and characteristics. With regard to gender, even if the different biases discussed tend to be more apparent in female subgroups, one can see that the overall variation in responses in the dataset did not have much to do with gender. Much more influential than gender is the age of investors and amount of experience in the financial market. It must be said that answers for the questions on Dunning-Kruger, gender, investment, and Iran's economy were very similar across different investors in the context of a two-dimensional PCA. Figure 3: Contribution of variables in PCA. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Eigenvalue** & **Percentage of Variance** & **Cumulative Percentage of Variance** \\ \hline comp 1 & 2.3832053 & 19.860044 & 19.86004 \\ \hline comp 2 & 1.7042055 & 14.201712 & 34.06176 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Principal components eigenvalues. Two dimensional-visualisation of PCA (Figure 4) can help identify the strength and direction of biases and other variables so that they can be grouped. Positively related variables are grouped together, while negatively related variables are positioned on the opposite sides of the plot origin in opposing quadrants. The distance between variables and the origin determines the quality of the variables on the factor map. Variables that are far away from the origin are well represented on the factor map. Thus, one can conclude that the perception of Iran's economy is negatively correlated with most factors. The reaction for the bandwagon effect and availability cascade is very similar. As well as PCA dimensions reductions, individual data can be clustered with k-means and visualised in 2D space (Figure 5). With an optimal number of clusters k = 3 selected using the dendrogram approach, one can check the groupings and separation of variables. K-means clustering with Euclidean distance showed that confirmation bias and investment amount form one group; gender, age and assessment of Iran's economy form the second group; and the remaining biases (availability, bandwagon, loss aversion, hot-hand, Dunning-Kruger and gambler's), together with experience, form the third group. This partitioning is stable both in k-means and in the dendrogram, while the silhouette statistic proves its high quality. Feature Importance, a method for diagnosing the impact of a given variable on cluster formation, plays a role similar to significance in parametric statistics. One can see that the most influential factor for partitioning is loss aversion bias, followed by experience and gambler's bias. The three least important factors are gender, age, and perception of Iran's economy, and they build their own cluster. The conclusion is that diversification of investors likely results mostly from experience and somehow inherited risk aversion, while gender and age are not decisive factors. Figure 4: Quality and direction of representation for variables.