i. A variable whose possible outcomes are coded as a "1" or a "0" is called a dummy variable. ii. A dummy variable is added to the regression equation to control for error. iii. If the null hypothesis $\beta$₄ = 0 is not rejected, then the independent variable X₄ has no effect in predicting the dependent variable. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

- A dummy variable is indeed a variable that takes the value of 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. It is used in regression analysis to represent categorical variables.- The purpose of adding a dummy variable to a regression equation is not to control for error but to control for the effect of categorical variables. It allows the model to differentiate between different groups or conditions represented by the categorical variable.- If the null hypothesis that the coefficient of an independent variable is equal to zero is not rejected, it suggests that the independent variable does not have a statistically significant effect on the dependent variable in the context of the model. This means the variable does not contribute to explaining the variation in the dependent variable, assuming the model is correctly specified and all relevant variables are included.

I a Variable Whose Possible Outcomes Are Coded as a "1