Class 17 (Categorical X)

Indicator Variable

• A categorical, explanatory _____ that serves as an _____ to 2 levels or options that a categorical X has

  • Ex: CatF = 0 if a cat is a male and CatF = 1 if a cat is a female

LSLR Line

• A fitted model that minimizes the data and the line

• Beta terms get hats, residual goes away

Intercept Interpretation

“We predict the average [Y Value] for [Value of IndiCatX = 0] to be beta-hat-sub0.”

Level 2 Interpretation

“We would predict the average [Y Value] for [Value of IndiCatX = 1] to be beta-hat-sub0 + beta-hat-sub1.”

Slope Interpretation

“The predicted [Value of Y] for [Level 2 Value] is [lower/higher than] for [Level 1 Value], on average.”

Categorical Explanatory Variables

• Has k levels

• Only has k - 1 coefficients being estimated in the model

  • One of the levels of the variable is consumed by the intercept of the model (beta-hat-sub0)

Baseline

The level of the categorical explanatory variable that is consumed by the intercept of the model (beta-hat-sub0)

Multiple Regression Model

• Has more beta terms (coefficients) than just the slope and intercept

• This model is not always a line

Coefficient of Numeric

“After controlling for [Categorical X], if [object of X] increases by 1 [units], we predict the average number of [Y] [increases/decreases] by [Y Units].”

Coefficient of Categorical

“After controlling for [Numeric X], we predict [object of X] is [less/more] than [beta-hat-sub2 = 0], on average.”