When using the model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$ for one qualitative independent variable with a $0 - 1$ coding convention, $\beta _ { 1 }$ represents the difference between the mean responses for the level assigned the value 1 and the base level.

Question

Quizplus · Accepted Answer

In this model, $\beta_1$ captures the effect of changing the qualitative independent variable from the base level (coded as 0) to the other level (coded as 1), thus representing the difference in mean responses between these two levels.

When Using the Model E(y)=β0+β1xE ( y ) = \beta _ { 0 } + \beta _ { 1 } xE(y)=β0​+β1​x

When Using the Model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x$