Question

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.

Answer 1

Ans:

a)Correlation or relationship(negative or positive) between two variables does not mean causation.

Correlation is based on observed data,but causation is based on experiments.

b)The lurking variable is the extraneous variable which is not being considered in the study but it does affect the response variable.It may be quantitative or qualitative variable.

c)Residuals may be positive or negative,sum of all residuals is always 0.

Answer 2

1. "A negative relationship is always due to causation." Error: The error in this statement is the assumption that a negative relationship between variables implies causation.

Explanation: A negative relationship between variables means that as one variable increases, the other variable tends to decrease. However, correlation does not imply causation. Just because two variables have a negative relationship does not mean that one variable causes the other to change. There may be other factors or variables at play that are influencing the observed relationship. Causation requires further evidence and analysis beyond just observing a negative relationship.

1. "A lurking variable is always a quantitative variable." Error: The error in this statement is the assumption that lurking variables are always quantitative.

Explanation: A lurking variable is a variable that is not included in the analysis but affects the relationship between the variables under study. Lurking variables can be either quantitative or qualitative (categorical). They can represent any factor or characteristic that influences the observed relationship. For example, in a study investigating the relationship between income and education level, age could be a lurking variable. Age is a qualitative variable, but it can still have an impact on the relationship between income and education. Therefore, lurking variables can be quantitative or qualitative, depending on the context.

1. "If the residuals are all negative, this implies that there is a negative relationship between the response variable and the explanatory variable." Error: The error in this statement is the assumption that the sign of the residuals determines the direction of the relationship between variables.

Explanation: The sign of the residuals (the differences between the observed and predicted values in a regression analysis) does not determine the direction of the relationship between the response variable and the explanatory variable. The residuals represent the unexplained variation in the data and can be positive or negative. They do not provide information about the direction of the relationship. The relationship between variables is determined by the coefficients or slopes in the regression model. The sign of the coefficients indicates the direction of the relationship, not the sign of the residuals. Therefore, the statement is incorrect.