Data

The GAM of Furrycat’s data shows a strong relationship between speed and courage.

model <- gam(
  formula = speed ~
    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:
## speed ~ 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) 2.0764512  0.0008771 2367.492   <2e-16 ***
## armor       0.0051265  0.0026512    1.934   0.0539 .  
## ---
## 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    0.688   0.407    
## s(fortitude)     1.000  1.000    0.950   0.330    
## s(dexterity)     1.000  1.000    0.078   0.780    
## s(endurance)     1.008  1.016    0.341   0.569    
## s(intellect)     1.000  1.000    0.843   0.359    
## s(cleverness)    1.000  1.000    0.015   0.903    
## s(courage)       7.109  8.114 1370.592  <2e-16 ***
## s(dependability) 6.530  7.695    1.304   0.226    
## s(power)         1.000  1.000    1.300   0.255    
## s(fierceness)    1.560  1.944    0.380   0.631    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.984   Deviance explained = 98.5%
## GCV = 0.00022148  Scale est. = 0.0002084  n = 410

This is easy to see with the graph.

ggplot(normalized_df, aes(x = courage, y = speed)) +
  geom_point() +
  ggtitle("Courage vs Speed")

And GAM shows a linear relationship.

plot(model, select = 7)

The linear model shows high correlation and low residuals.

model <- lm(speed ~ courage, data = normalized_df)
summary(model)

## 
## Call:
## lm(formula = speed ~ courage, data = normalized_df)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.176398 -0.002232  0.000720  0.003282  0.198662 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.488e+00  3.350e-03   742.8   <2e-16 ***
## courage     -9.840e-04  7.748e-06  -127.0   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01774 on 408 degrees of freedom
## Multiple R-squared:  0.9753, Adjusted R-squared:  0.9753 
## F-statistic: 1.613e+04 on 1 and 408 DF,  p-value: < 2.2e-16

And looks like this.

Speed Analysis

Data

Conclusion