An estimated multiple regression model has the form $\hat { y } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 } + \hat { \beta } _ { 2 } x _ { 2 } .$ Which of the following best describes $\hat { \beta } _ { 2 }$ ?
A)We estimate for each one unit increase in x2, that y will increase by $\hat { \beta } _ { 2 }$ units, on average.
B)Whilst holding x1 constant, we estimate for each one unit increase in x2, that y will increase by $\hat { \beta } _ { 2 }$ units, on average.
C)Whilst holding x2 constant, we estimate for each one unit increase in x1, that y will increase by $\hat { \beta } _ { 2 }$ units, on average
D)Whilst holding x1 constant, we estimate for each one unit increase in x2, that y will increase by $\hat { \beta } _ { 2 }$ units, on average .

Question

Quizplus · Accepted Answer

$\hat { \beta } _ { 2 }$ represents the estimated change in the dependent variable $y$ for a one-unit increase in $x_2$, assuming that $x_1$ (the other independent variable) is held constant. This is a fundamental interpretation of coefficients in multiple regression analysis.

An Estimated Multiple Regression Model Has the Form 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​.

An Estimated Multiple Regression Model Has the Form $\hat { y } = \hat { \beta } _ { 0 } + \hat { \beta } _ { 1 } x _ { 1 } + \hat { \beta } _ { 2 } x _ { 2 } .$