Question

Which of the following statements are true? I. In the computer output for regression, s is the estimator of o, the standard deviation of the response variable. II. A null hypothesis that B1 = 0, if true, implies that there's no correlation between the x and y variables. III. The t test for the slope of a regression line is always two-sided.

a) l only
b) ll only
c) III only
d) I and II only
e) II and III only

Answer 1

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.