Question

a nutritionist collects data from 25 popular breakfast cereals. for each cereal, the number of calories per serving is plotted on the x - axis against the number of milligrams of sodium on the y - axis. the value of r for the resulting scatterplot is 0.83. which of the following is a correct interpretation of this value?
each additional calorie is predicted to add approximately 0.83 mg of sodium.
there is a positive relationship between calories and sodium. the relationship is weak.
there is a positive relationship between calories and sodium. the relationship is strong.
as the number of calories increases, the amount of sodium decreases. the relationship is strong.

Explanation:

• The correlation coefficient \(r = 0.83\).
• The sign of \(r\) (positive in this case) indicates the direction of the relationship. A positive \(r\) means as one variable (calories) increases, the other variable (sodium) also tends to increase.
• The magnitude of \(r\): The value of \(r\) ranges from \(- 1\) to \(1\). Values close to \(1\) (or \(-1\)) indicate a strong linear relationship. Since \(|r|=0.83\) which is close to \(1\), the relationship is strong.

Answer:

There is a positive relationship between calories and sodium. The relationship is strong.