Final answer:
For the empty model to be completely true in linear regression analysis, the slope coefficient b1 would have to equal 0, indicating that the independent variable has no effect on the dependent variable.
Step-by-step explanation:
The question: What does b1 have to equal for the empty model to be completely true? pertains to the field of statistics within mathematics, specifically to linear regression analysis.
In the context of a simple linear regression model, the equation is typically represented as y = b0 + b1*x + e, where y is the dependent variable, x is the independent variable, b0 is the intercept, b1 is the slope, and e is the error term.
The empty model, also known as the null model, assumes that none of the independent variables included are predictive of the outcome variable. In other words, the model assumes that the dependent variable's mean is a suitable estimate for every case.
For the empty model to be completely true, meaning that the independent variable has no effect on the dependent variable, the slope coefficient b1 would have to equal 0. In this scenario, the model simplifies to y = b0 + e, indicating that all variations in y are due to random error e rather than changes in the independent variable x.