Question

In a backwards selection process all variables with p-values from the t-tests > 0.05 get removed. A new regression analysis is run with the remaining variables. the variable with the highest p-value from the t-tests would get removed no matter what its p-value. A new regression analysis is run with the remaining variables. the variable with the highest p-value from the t-tests would get removed only if its p-value is > 0.05. A new regression analysis is run with the remaining variables. no variables are ever removed from a regression analysis no matter what their p-values from the t-tests are. You can only remove a variable if there is a non-statistical reason to do so.

Answer 1

In backward elimination method one variable is removed at a time based on the significance of that variable. So, in this method, the variable with highest p-value will be removed as highest p-value implies lowest significance. It is irrespective of the p-value obtained as long as it is higher than the level of significance.  

Here, the level of significance is assumed to be 0.05. So, a new regression analysis is run with the remaining variables. The variable with the highest p-value from the t-tests would get removed only if its p-value is > 0.05.