Data

A GAM of Furrycat’s data shows a strong relationship between action and both dexterity and intellect.

model <- gam(
  formula = action ~
    s(hardiness) +
    s(fortitude) + 
    s(dexterity) + 
    s(endurance) +
    s(intellect) + 
    s(cleverness) + 
    s(courage) + 
    s(dependability) +
    s(power) +
    s(fierceness) +
    armor,
  family = gaussian(),
  data = normalized_df
)

## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## action ~ s(hardiness) + s(fortitude) + s(dexterity) + s(endurance) + 
##     s(intellect) + s(cleverness) + s(courage) + s(dependability) + 
##     s(power) + s(fierceness) + armor
## 
## Parametric coefficients:
##              Estimate Std. Error   t value Pr(>|t|)    
## (Intercept) 5190.1706     0.3615 14356.804   <2e-16 ***
## armor         -0.4929     1.1855    -0.416    0.678    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                    edf Ref.df         F p-value    
## s(hardiness)     1.000  1.000 2.000e-03  0.9607    
## s(fortitude)     1.462  1.814 3.070e-01  0.7652    
## s(dexterity)     1.524  1.903 4.223e+06  <2e-16 ***
## s(endurance)     1.505  1.855 6.190e-01  0.5894    
## s(intellect)     6.080  7.219 5.221e+04  <2e-16 ***
## s(cleverness)    1.030  1.056 2.300e-02  0.9065    
## s(courage)       2.064  2.618 1.164e+00  0.4254    
## s(dependability) 1.000  1.000 4.000e-03  0.9468    
## s(power)         1.000  1.000 6.590e-01  0.4174    
## s(fierceness)    1.000  1.000 3.611e+00  0.0581 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## GCV = 33.813  Scale est. = 32.191    n = 410

And the GBM shows linear relationships.

plot(model, select = 3)

plot(model, select = 5)

The linear model shows high correlation and low residuals.

model <- lm(action ~ dexterity + intellect, data = normalized_df)
summary(model)

## 
## Call:
## lm(formula = action ~ dexterity + intellect, data = normalized_df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -40.166  -4.450  -0.449   4.802   8.619 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 41.681785   0.572528    72.8   <2e-16 ***
## dexterity   14.957012   0.002944  5081.3   <2e-16 ***
## intellect    2.993910   0.002708  1105.5   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.715 on 407 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 6.126e+07 on 2 and 407 DF,  p-value: < 2.2e-16

And looks like this.

The residuals suggest that some of the error may be due to rounding.

Action Analysis

Data

Conclusion