Data

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

model <- gam(
  formula = health ~
    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:
## health ~ 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) 7660.3918     0.3378 22676.340   <2e-16 ***
## armor         -0.9996     0.9550    -1.047    0.296    
## ---
## 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 1.133e+07  <2e-16 ***
## s(fortitude)     1.000  1.000 1.095e+00  0.2960    
## s(dexterity)     1.000  1.000 3.708e+05  <2e-16 ***
## s(endurance)     1.000  1.000 1.116e+00  0.2914    
## s(intellect)     4.157  5.132 9.740e-01  0.4435    
## s(cleverness)    1.000  1.000 3.360e-01  0.5627    
## s(courage)       1.612  2.012 4.520e-01  0.6482    
## s(dependability) 1.000  1.000 6.133e+00  0.0137 *  
## s(power)         1.000  1.000 5.452e+00  0.0201 *  
## s(fierceness)    1.000  1.000 3.757e+00  0.0534 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =      1   Deviance explained =  100%
## GCV = 28.036  Scale est. = 26.841    n = 370

And GAM shows a linear relationships.

plot(model, select = 1)

plot(model, select = 3)

The linear model shows high correlation and low residuals.

model <- lm(health ~ hardiness + dexterity, data = normalized_df)
summary(model)

## 
## Call:
## lm(formula = health ~ hardiness + dexterity, data = normalized_df)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -8.686 -4.792  0.466  4.588  8.216 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 40.904833   0.722564   56.61   <2e-16 ***
## hardiness   14.961766   0.002567 5828.13   <2e-16 ***
## dexterity    2.991161   0.002784 1074.51   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.254 on 367 degrees of freedom
## Multiple R-squared:      1,  Adjusted R-squared:      1 
## F-statistic: 6.629e+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.

Health Analysis

Data

Conclusion