For Exercises 2.77 to 2.79, see page 101; and for 2.80, see page 102.

Question 2.81

2.81 What's wrong?

Each of the following statements contains an error. Describe each error and explain why the statement is wrong.

  1. A negative relationship is always due to causation.
  2. A lurking variable is always a quantitative variable.
  3. If the residuals are all negative, this implies that there is a negative relationship between the response variable and the explanatory variable.

2.81

(a) Whether the relationship is negative or positive does not tell us anything as to whether or not there is causation. (b) A lurking variable can be categorical. (c) It is actually impossible for all the residuals to be negative. Even if many of the residuals are negative, this tells us nothing regarding the relationship (positive or negative) of the variables. We need to look at the slope to determine if the relationship is positive or negative.