Methods - Chapter 13

Multiple Linear Regression Model

y = β₀ + β₁x₁ + β₂x₂ + … + β_px_p + ε

Multiple Regression Equation

E(y) = β₀ + β₁x₁ + β₂x₂ + … + β_px_p

Estimated Multiple Regression Equation

ŷ = b₀ + b₁x₁ + b₂x₂ + … + b_px_p

Least Squares Criterion

minΣ(yi - ŷi)²; minimize the error between the actual data value and the regression result

Multiple Regression F Test

determines whether a significant relationship exists between y and the set of all independent variables; tests for overall significance.

Multiple Regression T Test

determines whether a significant relationship exists between y and x₁, x₂ etc; tests for individual significance of each variable.

Multiple Significance Hypotheses

H₀: β_i = 0 (all slopes β₁, β₂, etc.), H_A: β_i ≠ 0

T Statistic

= MSR / MSE

Multicollinearity

when some independent variables are HIGHLY correlated => essentially a repeat of a variable, useless. Choose the better one out of those variables, the one with higher significance.

Correlation Check

always check the correlation between all independent variables; avoid correlations >0.7 that cause multicollinearity.

Dummy Variable

the variable that equals 1, indicating a value that belongs in a categorical group.

R² Adjusted

R² adjusted for the number of independent variables = 1 - (1-r²)(n-1/n-k-1), most reliable for multi regression model.