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) 2.0717581  0.0009879 2097.188   <2e-16 ***
## armor       0.0056898  0.0028213    2.017   0.0445 *  
## ---
## 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    0.747   0.388    
## s(fortitude)     1.000  1.000    1.081   0.299    
## s(dexterity)     1.000  1.000    0.022   0.883    
## s(endurance)     1.173  1.325    0.600   0.599    
## s(intellect)     1.810  2.293    0.765   0.396    
## s(cleverness)    1.000  1.000    0.299   0.585    
## s(courage)       6.974  7.999 1140.548  <2e-16 ***
## s(dependability) 6.511  7.673    1.307   0.233    
## s(power)         1.000  1.000    1.114   0.292    
## s(fierceness)    1.152  1.287    0.090   0.803    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.982   Deviance explained = 98.3%
## GCV = 0.00024299  Scale est. = 0.00022682  n = 370

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 
## -0.176062 -0.002234  0.000852  0.003135  0.198289 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.487e+00  3.730e-03   666.7   <2e-16 ***
## courage     -9.821e-04  8.544e-06  -114.9   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01862 on 368 degrees of freedom
## Multiple R-squared:  0.9729, Adjusted R-squared:  0.9728 
## F-statistic: 1.321e+04 on 1 and 368 DF,  p-value: < 2.2e-16

And looks like this.

Speed Analysis

Data

Conclusion