Given the multiple linear regression equation, $\hat { y } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 } + \hat { \beta } _ { 2 } x _ { 2 } ,$ the value of $\hat { \beta } _ { 2 }$ is the estimated average increase in y for a one unit increase in x2, whilst holding x1 constant.

Question

Quizplus · Accepted Answer

The coefficient $\hat { \beta } _ { 2 }$ in a multiple linear regression equation represents the estimated change in the dependent variable ($\hat { y }$) for a one-unit increase in the independent variable $x_2$, assuming all other variables in the model are held constant.

Given the Multiple Linear Regression Equation y^=β^0+β^1x1+β^2x2,\hat { y } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 } + \hat { \beta } _ { 2 } x _ { 2 } ,y^​=β^​0​+β^​1​x1​+β^​2​x2​,

Given the Multiple Linear Regression Equation $\hat { y } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 } + \hat { \beta } _ { 2 } x _ { 2 } ,$