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

Multiple Choice

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 .