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) 5560.4334     0.4724 11770.36   <2e-16 ***
## armor         -0.3971     1.7229    -0.23    0.818    
## ---
## 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   0.961    
## s(fortitude)     4.183  5.192 8.270e-01   0.486    
## s(dexterity)     1.876  2.396 3.243e+06  <2e-16 ***
## s(endurance)     1.299  1.530 5.220e-01   0.681    
## s(intellect)     1.000  1.000 3.403e+05  <2e-16 ***
## s(cleverness)    1.000  1.000 1.610e-01   0.688    
## s(courage)       2.014  2.550 9.780e-01   0.514    
## s(dependability) 4.860  5.956 6.160e-01   0.693    
## s(power)         1.000  1.000 3.580e-01   0.550    
## s(fierceness)    1.000  1.000 2.116e+00   0.147    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## GCV =  34.48  Scale est. = 32.501    n = 370

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 
## -40.146  -4.431   0.289   4.816   8.919 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 41.632510   0.667900   62.33   <2e-16 ***
## dexterity   14.956091   0.003296 4537.54   <2e-16 ***
## intellect    2.995038   0.002906 1030.49   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.738 on 367 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 5.081e+07 on 2 and 367 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