Statistics for Business: Decision Making and Analysis, 3rd Edition

... sampled from a normal distribution with mean 0 and equal variance σ_∊².

Multiple Regression Model

The observed response Y is linearly related to k explanatory variables X₁, X₂, ⋅, and X_k by the equation

$$Y={\beta }_0+{\beta }_1{X}_1+{\beta }_2{X}_2+\cdots +{\beta }_k{X}_k+\epsilon ,\epsilon ~N\left(0, {\sigma }_{\epsilon }{2}^{}\right)$$

The unobserved errors ∊ in the model have mean 0 and

1. are independent of one another,

2. have equal variance σ²_∊, and

3. are normally distributed around the regression equation.

k

The number of explanatory variables in the multiple regression. (k = 1 in simple regression.)

The multiple regression model provides another way to think about the errors in regression. The SRM says that one explanatory variable X is associated with Y through a linear equation,

$$Y={\mu }_{y|x}+\epsilon \text{with}{\mu }_{y|x}={\beta }_0+{\beta }_{1}X$$

Only X systematically affects ...