Question

More hot dogs Refer to Exercise $19$

a. Explain why it isn’t correct to say that the correlation is $0.87mg/cal$

b. What would happen to the correlation if the variables were reversed on the scatterplot? Explain your reasoning.

c. What would happen to the correlation if sodium was measured in grams instead of milligrams? Explain your reasoning.

Short answer

Part (a) This statement is not true.

Part (b) The correlation remains the same.

Part (c) The correlation will remain the same.

Step-by-step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

We must determine why it is incorrect to state that the correlation is $0.87mg/cal$ in order to answer this question. As a result, we can't state the correlation is $0.87mg/ca$l because the units $"mg/cal"$ were allocated to the correlation. Correlation, on the other hand, is never related with units. As a result, this statement is false.

Part (b) Step 1: Explanation

According to the question, we must determine what would happen to the correlation if the variables on the scatterplot were reversed. The correlation, as we all know, evaluates the degree of linearity between two variables. As a result, if the variables on the scatterplot are flipped, the amount of linearity between the two variables is unaltered, and the correlation is unaffected as well.

Part (c) Step 1: Explanation

We must determine what would happen to the association if sodium was measured in grammes rather than milligrammes, as stated in the question. The correlation, as we all know, evaluates the degree of linearity between two variables. As a result, measuring sodium in grammes rather than milligrammes has no effect on the link between the variables because the relationship remains the same. As a result, the level of linearity in the relationship between the variables remains unchanged, and the correlation remains unchanged.