Question

algebra 1 unit 3 section c checkpoint

1. during the autumn, a canadian citys number of flu cases and sales of sandals are recorded. a linear model is fit with a correlation coefficient of ( r=-0.24 ).

a. classify the relationship as strong or weak and as positive or negative.
b. do you think the relationship is causal? explain your reasoning.

Explanation:

Step1: Analyze the correlation coefficient's magnitude

The correlation coefficient \( r=-0.24 \). The magnitude \( |r| = 0.24 \). Since \( 0<|r|<0.5 \), the relationship is weak.

Step2: Analyze the sign of the correlation coefficient

The sign of \( r \) is negative (\( r=-0.24 \)), so the relationship is negative.

Step3: Consider causality

Causality implies that one variable directly causes the other. Flu cases are related to factors like virus spread, immunity etc. Sandal sales are related to weather (warmer weather might lead to more sandal sales). There is no direct causal link between flu cases and sandal sales. Just because there is a (weak) correlation (negative in this case) does not mean one causes the other.

Answer:

a. The relationship is weak and negative.
b. No, the relationship is not causal. Flu cases are influenced by health - related factors (e.g., virus transmission, immunity) and sandal sales are influenced by weather - related factors (e.g., temperature). There is no direct causal mechanism between the number of flu cases and sandal sales. A correlation (even if it existed in a stronger form) does not imply causation.