Model

The mathematical models used are the Gaussian model and the categorical model.

Gaussian:

• Assumes the relationship between the independent variables and dependent outcome is linear, which also supports the assumption that the error in the observed and perdicted values that occour when applying the model to new data are distributed proportionately across the range of data

Categorical:

• Used when the dependent variables is categorical, which can ultimately help predict the probability of each outcome per category; you can also compare the results across each category to see the difference in relationships and investigate other possible factors

\[ \text{Technology Amount} = \beta_0 + \beta_1 \cdot \text{Cranial Capacity} + \beta_2 \cdot \text{Manual Dexterity} + \epsilon \]

\[ \log \left( \frac{P(\text{Intermediate})}{P(\text{Simple})} \right) = \beta_{0,\text{Intermediate}} + \beta_{1,\text{Intermediate}} \cdot \text{Cranial Capacity} + \beta_{2,\text{Intermediate}} \cdot \text{Manual Dexterity} \]

\[ \log \left( \frac{P(\text{Complex})}{P(\text{Simple})} \right) = \beta_{0,\text{Complex}} + \beta_{1,\text{Complex}} \cdot \text{Cranial Capacity} + \beta_{2,\text{Complex}} \cdot \text{Manual Dexterity} \]

Evaluating Bias using Distributions of Observed vs Relevant Data:

Characteristic	Beta	95% CI 1
Cranial_Capacity	0.00	0.00, 0.00
action_var_num	1.2	1.1, 1.2
1 CI = Credible Interval