Final answer:
In regression analysis, 's' is indeed the estimator for the standard deviation of the error term, and a null hypothesis stating that the slope coefficient equals zero would imply no correlation between the explanatory and dependent variables. Additionally, the t-test for the slope coefficient is typically two-sided. Hence, the true statements are II and III only.
Step-by-step explanation:
The statements in question are related to the interpretation of computer output for regression analysis.
Statement I holds that s is the estimator of σ, the standard deviation of the response variable. This is true because in regression output, s stands for the standard error of the residuals, which estimates the standard deviation of the error term σ in the population regression equation.
Statement II suggests that if the null hypothesis that B1 = 0 is true, it implies there's no correlation between the x and y variables. This is true as well because if there is no slope, it means that changes in x do not predict changes in y, suggesting no linear relationship.
Statement III states that the t-test for the slope of a regression line is always two-sided. This is true because we usually are interested in testing whether there is a positive or negative linear relationship, rather than testing in a single direction only.
Therefore, the correct answer that includes all the true statements is option (e): II and III only.