Engine Displacement & Fuel Economy

Trained using 2010 data and tested using 2011 data.

Training Using a Linear Model

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FuelEconomy.lm <- lm(FE ~ EngDispl, data = cars2010)
mse1.lm <- mean(residuals(FuelEconomy.lm)^2)
print(rmse1.lm <- sqrt(mse1.lm))

[1] 4.620076

summary(FuelEconomy.lm) gives R2 = 0.6196

Training Using a Quadratic Model

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FuelEconomy.q <- lm(FE ~ EngDispl + I(EngDispl^2), data = cars2010)
mse2.lm <- mean(residuals(FuelEconomy.q)^2)
print(rmse2.lm <- sqrt(mse2.lm))

[1] 4.234826

summary(FuelEconomy.q) gives R2 = 0.6801

Testing Using the Quadratic Model

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# R2
errors <- (DataFrame2011$y2 - DataFrame2011$y1) 
1 - sum(errors^2)/sum((DataFrame2011$y2 - mean(DataFrame2011$y2))^2)
# RMSE
sqrt(mean((DataFrame2011$y2 - DataFrame2011$y1)^2))

R2 = 0.736, RMSE = 4.716

Testing Using the Linear Model

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# R2
errors.lm <- (DataFrame2011_lm$y2 - DataFrame2011_lm$y1)
1 - sum(errors.lm^2)/sum((DataFrame2011_lm$y2 - mean(DataFrame2011_lm$y2))^2
# RMSE
sqrt(mean((DataFrame2011_lm$y2 - DataFrame2011_lm$y1)^2)

R2 = 0.684, RMSE = 5.163