Consider the multiple regression model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \cdots + \beta _ { k } x _ { k } + \varepsilon$
) When using this model,we assume that at any given combination of values of x₁,x₂,... ,x_k the population of potential error term values has a ________ distribution.

Question

Consider the multiple regression model

y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \cdots + \beta _ { k } x _ { k } + \varepsilon

) When using this model,we assume that at any given combination of values of x₁,x₂,... ,x_k the population of potential error term values has a ________ distribution.

Quizplus · Accepted Answer

The assumption for the error terms in a multiple regression model is that they are normally distributed for any given combination of the independent variables. This is a key assumption for the validity of statistical tests on the coefficients.

Consider the Multiple Regression Model y=β0+β1x1+β2x2+⋯+βkxk+εy = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \cdots + \beta _ { k } x _ { k } + \varepsilony=β0​+β1​x1​+β2​x2​+⋯+βk​xk​+ε

Consider the Multiple Regression Model $y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \cdots + \beta _ { k } x _ { k } + \varepsilon$