Wrapping up linear regression

Supervised Learning in R: Regression

Nina Zumel and John Mount

Win-Vector, LLC

Pros and Cons of Linear Regression

Pros
- Easy to fit and to apply
- Concise
- Less prone to overfitting

Pros and Cons of Linear Regression

Pros
- Easy to fit and to apply
- Concise
- Less prone to overfitting
- Interpretable

Call:
lm(formula = blood_pressure ~ age + weight, data = bloodpressure)

Coefficients:
(Intercept)          age       weight  
    30.9941       0.8614       0.3349

Pros and Cons of Linear Regression

Pros
- Easy to fit and to apply
- Concise
- Less prone to overfitting
- Interpretable
Cons
- Can only express linear and additive relationships

Collinearity

Collinearity -- when input variables are partially correlated.

Call:
lm(formula = blood_pressure ~ age + weight, data = bloodpressure)

Coefficients:
(Intercept)          age       weight  
    30.9941       0.8614       0.3349

Collinearity

Collinearity -- when variables are partially correlated.
Coefficients might change sign

Call:
lm(formula = blood_pressure ~ age + weight, data = bloodpressure)

Coefficients:
(Intercept)          age       weight  
    30.9941       0.8614       0.3349

Collinearity

Collinearity -- when variables are partially correlated.
Coefficients might change sign
High collinearity:
- Coefficients (or standard errors) look too large
- Model may be unstable

Call:
lm(formula = blood_pressure ~ age + weight, data = bloodpressure)

Coefficients:
(Intercept)          age       weight  
    30.9941       0.8614       0.3349

Coming Next

Evaluating a regression model
Properly training a model

Let's practice!

Supervised Learning in R: Regression

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