Questions: For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in one serving of 77 breakfast cereals produced the regression model Potassium = 38+27 Fiber. From this model you can estimate a cereal's potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual? What does it mean to say that a cereal has a residual of -22 ? What does it mean to say that a cereal has a residual of -22 ? A. A residual of -22 means that particular cereal has 22 mg more potassium than the model predicts. B. A residual of -22 means that particular cereal has 22 mg less potassium than the model predicts. C. A residual of -22 means that particular cereal has 22 g more fiber than the model expects. D. A residual of -22 means that particular cereal has 22 g less fiber than the model expects.

For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in one serving of 77 breakfast cereals produced the regression model Potassium = 38+27 Fiber. From this model you can estimate a cereal's potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual? What does it mean to say that a cereal has a residual of -22 ? What does it mean to say that a cereal has a residual of -22 ? A. A residual of -22 means that particular cereal has 22 mg more potassium than the model predicts. B. A residual of -22 means that particular cereal has 22 mg less potassium than the model predicts. C. A residual of -22 means that particular cereal has 22 g more fiber than the model expects. D. A residual of -22 means that particular cereal has 22 g less fiber than the model expects.
Transcript text: For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in one serving of 77 breakfast cereals produced the regression model Potassium $=38+27$ Fiber. From this model you can estimate a cereal's potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residual? What does it mean to say that a cereal has a residual of -22 ? What does it mean to say that a cereal has a residual of -22 ? A. A residual of -22 means that particular cereal has 22 mg more potassium than the model predicts. B. A residual of -22 means that particular cereal has 22 mg less potassium than the model predicts. C. A residual of -22 means that particular cereal has 22 g more fiber than the model expects. D. A residual of -22 means that particular cereal has 22 g less fiber than the model expects.
failed

Solution

failed
failed

Solution Steps

To solve this problem, we need to understand the concept of residuals in the context of a regression model. A residual is the difference between the observed value and the value predicted by the model. If a cereal has a residual of -22, it means the observed potassium content is 22 milligrams less than what the model predicts.

Solution Approach
  1. Identify the regression model: Potassium = 38 + 27 * Fiber.
  2. Understand that a residual of -22 means the observed potassium content is 22 milligrams less than the predicted value.
  3. Therefore, the correct interpretation is that the cereal has 22 mg less potassium than the model predicts.
Step 1: Understand the Regression Model

The regression model given is: \[ \text{Potassium} = 38 + 27 \times \text{Fiber} \]

Step 2: Calculate Predicted Potassium Content

For a cereal with a fiber content of 5 grams: \[ \text{Predicted Potassium} = 38 + 27 \times 5 = 38 + 135 = 173 \, \text{mg} \]

Step 3: Interpret the Residual

A residual of -22 means the observed potassium content is 22 milligrams less than the predicted value: \[ \text{Observed Potassium} = 173 \, \text{mg} - 22 \, \text{mg} = 151 \, \text{mg} \]

Step 4: Answer the Multiple-Choice Question

A residual of -22 means that the observed potassium content is 22 milligrams less than the model predicts. Therefore, the correct interpretation is: \[ \boxed{\text{B}} \]

Final Answer

The answer is \(\boxed{\text{B}}\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
In the economic production quantity (EPQ) model, costs are analogous to ordering costs.
failedAnswered
In the reaction between HNO3 and Ba(OH)2 (assume complete reaction of the Ba(OH)2), the spectator ions are A Ba2+ and NO3- B H+and NO3 - C H+and OH- D Ba2+ and OH-
failedAnswered
What is the definition of a midpoint in a segment? A point that divides the segment into two equal parts A point that is at the end of the segment A point that is outside the segment
failedAnswered
Week 1: Music and Education Read the article "Keeping Music Alive" under Learning Materials and watch the two short videos. Write a one-page summary of your understanding of how music can affect the human brain, emotions, learning and responding capacity. The national standards categorizes music in the classroom as creating, performing and responding. In your discussion, include how music is particularly capable of providing those experiences for children in the learning situation.
failedAnswered
A plain view arrest may be made without a warrant. (A) True (B) False