Question

A student says that the larger the absolute value of r​ is, the greater the probability that a change in the explanatory variable will cause a change in the response variable. What would you tell the​ student?

Answer 1

Answer:

Step-by-step explanation:

The student has a valid point but here's what I would tell him or her:

The larger the absolute value of r, the greater the probability that an increase in the value of the explanatory variable will cause an increase in the value of the response variable.

"r" here represents the correlation coefficient (Pearson's correlation coefficient) which shows the direction and strength of relationship between two variables.

The explanatory variable is the independent variable. It is the variable that places an effect on the other.

The response variable is the dependent variable. It is the variable which is observed for an effect.

When r is positive, it means that both variables move (increase or decrease) in the same direction. When the absolute value of r is large, it shows a great magnitude of change.

Answer 2

The r value is the correlation coefficient which gives the strength and direction of the relationship between two variables. Hence, the absolute value of r could tell the probability of change in the dependent variable due to the response variable.

• The Correlation Coefficient, r, is a measure of how strong and the nature of the association between two variables.

• Since the correlation Coefficient shows how changes in one variable affects the other, then we can deduce that greater values of r will lead to an increased probability of change.

Since, r values can be either positive or negative, the absolute value of r should be considered for negative association.

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