Question

the graph shows the volume of ice cubes versus temperature in degrees celsius. which statement is false? a. the data show a negative linear relationship. b. the correlation coefficient is close to zero. c. temperature is the explanatory variable. d. temperature is strongly correlated to the volume of ice cubes.

Explanation:

Step1: Analyze the scatter - plot

As the temperature increases, the volume of ice cubes decreases, showing a negative linear trend.

Step2: Evaluate each option

• Option A: Since the points follow a downward - sloping linear pattern, the data show a negative linear relationship. This is true.
• Option B: A correlation coefficient close to zero means little to no linear relationship. But here, there is a clear negative linear relationship, so the correlation coefficient is not close to zero. This statement is false.
• Option C: Temperature is likely to be the variable that affects the volume of ice cubes, so it is the explanatory variable. This is true.
• Option D: The points are closely clustered around a line, indicating a strong linear correlation between temperature and the volume of ice cubes. This is true.

Answer:

B. The correlation coefficient is close to zero.