The Bias-Variance Tradeoff

head(training_set)

type	year	make	model	trim	mileage	price
USED	2007	Honda	Accord	EX-L V-6	96715	12950
USED	2006	Honda	Accord	EX V-6	102644	10998
USED	2005	Honda	Accord	LX	111639	7688
USED	2001	Honda	Accord	EX	103771	5788
USED	2008	Honda	Accord	EX-L V-6	39029	16998
USED	2012	Honda	Accord	EX-L V-6	40131	19888

---

p <- ggplot(data = training_set, 
            aes(x = mileage, y = price)) +
  geom_point()
p

---

p + geom_smooth(method = "lm", 
                formula = y ~ 1 + x)

---

rmse <- function(pred, value) {
  sqrt(mean((pred - value)^2))
}

model_1 <- lm(price ~ 1 + mileage,
              data = training_set)
rmse(predict(model_1, training_set), training_set$price)

## [1] 2355

---

p + geom_smooth(method = "lm", 
                formula = y ~ 1 + x + I(x^2))

---

model_2 <- lm(price ~ 1 + mileage + I(mileage^2),
              data = training_set)
rmse(predict(model_2, training_set), training_set$price)

## [1] 2331

---

p + geom_smooth(method = "lm", 
                formula = y ~ 1 + x + I(x^2) + I(x^3) +
                  I(x^4) + I(x^5))

---

model_5 <- lm(price ~ 1 + mileage + I(mileage^2) +
              I(mileage^3) + I(mileage^4) + I(mileage^5),
              data = training_set)
rmse(predict(model_5, training_set), training_set$price)

## [1] 2142

Training vs. test error

c(
  rmse(predict(model_1, training_set), training_set$price),
  rmse(predict(model_1, test_set), test_set$price)
)

## [1] 2355 2464

c(
  rmse(predict(model_2, training_set), training_set$price),
  rmse(predict(model_2, test_set), test_set$price)
)

## [1] 2331 2337

c(
  rmse(predict(model_5, training_set), training_set$price),
  rmse(predict(model_5, test_set), test_set$price)
)

## [1] 2142 4715

---

p + geom_smooth(method = "lm", 
                formula = y ~ 1 + x + I(x^2) + I(x^3) +
                  I(x^4) + I(x^5)) +
  geom_point(data = test_set, color = "red")