In the preceding chapter, you developed four regression models to predict the outcomes of battles in which the Shu army uses head to head, surround, ambush, and fire attack methods. A sample regression model for each of the battle methods is provided to you in this chapter. For demonstration and consistency, these models will be used throughout the chapter. However, you are encouraged to substitute your own models from Chapter 5 into the calculations and activities in this chapter.
For the duration of this chapter, we will focus on employing our regression models to predict outcomes and to determine the feasibility of different attack strategies. Ultimately, you will need to decide on the best course of action for the Shu army. By the end of this chapter, you will be able to:
- Use regression models to predict outcomes
- Create your own custom functions to address specific needs
- Assess the viability of achieving the outcomes predicted by regression models
In this section, we will review each of the four regression models created in Chapter 5. This will refresh our memory and prepare us to use our models in developing and assessing potential strategies. Again, while these sample models will appear throughout this chapter, feel free to substitute your own models into any or all activities.
The following is a summary of the head to head model:
Our head to head regression model predicts the Shu army's performance rating based on the duration of battle and the number of Shu and Wei soldiers engaged. All of these coefficients, as well as the overall model, are statistically significant. The model explains 86% of the variance in performance rating. Therefore, 14% of the rating remains unaccounted for and unpredicted. Our head to head regression equation is:
Rating = 97 - 0.77 * duration + 0.00054 * Shu soldiers - 0.00028 * Wei soldiers
Recall that our dependent variable of Rating is represented numerically on a scale from 0 to 100. Consequently, the higher the value predicted by our regression model, the more confident we can be that our strategy will lead to victory. Conversely, a lower value would make us more certain that our strategy would lead to defeat. For instance, a value of 90 would indicate a higher likelihood of victory, while a value of 10 would indicate a higher likelihood of defeat. Keeping this in mind, let us analyze the coefficients in our head to head combat model.
In our equation, the duration coefficient of -0.77 indicates that the Shu army's chances of victory decrease rapidly as the length of a head to head conflict increases. The positive coefficient for Shu soldiers engaged implies that deploying more Shu soldiers leads to a higher prospect of victory. In contrast, the negative coefficient for Wei soldiers engaged suggests that the more Wei soldiers deployed, the lower the chances of victory for the Shu army. The intercept of 97 does not have a logical practical interpretation, but it is essential to making predictions with the model. This is true of the intercept in each of our sample models.
The following is a summary of the surround model:
Our surround method regression model predicts the Shu army's performance rating based on execution (successful or unsuccessful), the duration of battle, and the number of Shu and Wei soldiers engaged. All of these coefficients, as well as the overall model, are statistically significant. This model contains a remarkable 98% of the elements that predict the variance in performance rating when the surround strategy is employed. Our surround regression equation is:
Rating = 35 + 58 * execution - 0.15 * duration + 0.18 * Shu soldiers - 0.19 * Wei soldiers
Here, the 58 coefficient suggests that successful execution is not only critical, but likely necessary to predict victory. Recall that our SuccessfullyExecuted variable was categorical. It has been represented as 0 for no and 1 for yes. Accordingly, successful execution of the surround method will add 58 to our final rating prediction, whereas unsuccessful execution will contribute 0. Therefore, our predicted outcome weighs tremendously on whether or not we expect our forces to successfully execute the surround technique. Again, a shorter duration of battle is better. The coefficients for Shu and Wei soldiers engaged can be interpreted in similar fashion to our head to head model.
The following is a summary of the ambush model:
Our ambush method regression model predicts the Shu army's performance rating based on execution, duration, and the number of Shu and Wei soldiers engaged. All of these coefficients, as well as the overall model, are statistically significant. This model explains a formidable 92% of the variance in performance rating when the ambush strategy is employed. Our ambush regression equation is:
Rating = 56 + 44 * execution - 1.97 * duration + 0.0018 * Shu soldiers - 0.00082 * Wei soldiers
In this case, the rating prediction is also tied strongly to successful execution. Once again, the duration and number of Shu and Wei soldiers engaged can be interpreted in the same manner as our preceding models.
The following is a summary of the fire model:
Our fire attack regression model predicts the Shu army's performance rating based on execution, duration, and the interaction between the number of Shu and Wei soldiers engaged in battle. Here, it is not the raw number of soldiers for each side that impacts our prediction, but rather the relationship between them. All of the coefficients, as well as the overall model, are statistically significant. This model explains a solid 93% of the variance in performance rating when the fire attack strategy is employed. Our fire attack regression equation is:
Rating = 37 + 56 * execution - 1.24 * duration - 0.00000013 * soldiers interaction
In this equation, successful execution plays a critical role in explaining the battle rating, as does duration. Our interaction term suggests that the more soldiers involved in the battle, regardless of affiliation, the less likely our fire attack is to lead to victory. This makes sense considering that the fire attack, unlike our other methods, is a risky surprise tactic. Having too many Shu soldiers increases the visibility of our attack and the likelihood that our plans would be discovered. A similar condition arises from launching a fire attack on too many Wei soldiers. There would be more eyes to discover and arms to quash the surprise attack. Therefore, the interaction between the number of Shu and Wei soldiers involved in a fire attack must be balanced to optimize our impact and chances of success.