Consumer research on cold breakfast cereals recorded several nutritional aspects of each cereal’s ingredients as well as an overall health rating for each cereal.
This problem focuses on the variables “sugar” (number of grams of sugar per serving), “calories” (number of calories per serving), and “rating” (health rating on a scale from 1 to 100, where the healthiest cereals would receive scores close to 100). Health ratings were based on fat, sodium, fiber, carbohydrates, potassium, and other nutritional elements in addition to sugar.
The following colored scatterplot shows the relationships between sugar, calories and health rating. In this graph, sugar content (in grams) in marked on the horizontal axis, calories are graphed on the vertical axis, and health rating is described by the color of each cereal point plotted.
First, the impact of the number of calories on the health rating was studied, and the equation that best models the pattern of the relationship was found to be:
Predicted rating = -0.483 (number of calories) + 94
Then, the impact of the grams of sugar on the health rating was studied, and the equation that best models the pattern of the relationship was found to be:
Predicted rating = -2.43 (grams of sugar) + 60