Question

An analysis of the amount of fiber​ (in grams) and the potassium content​ (in milligrams) in servings of 77 breakfast cereals produced the regression model ModifyingAbove Potassium with caretequals37plus29Fiber. Explain what the slope means. Choose the correct answer below. A. The model predicts that cereals will have approximately 37 more grams of fiber for every additional milligram of potassium. B. The model predicts that cereals will have approximately 29 more grams of fiber for every additional milligram of potassium. C. The model predicts that cereals will have approximately 29 more milligrams of potassium for every additional gram of fiber. D. The model predicts that cereals will have approximately 37 more milligrams of potassium for every additional gram of fiber.

Answer 1

Answer:

C. The model predicts that cereals will have approximately 29 more milligrams of potassium for every additional gram of fiber.

Explanation:

The regression model is:

          $\widehat{Potassium}=37+29Fiber$

That model means that the average content of potassum (in mg) in breakfast cereals can be predicted from the content of fiber (in grams) by adding a constant of 37 to the product of 29 and the content of fiber.

Thus, the graphs of the content of potassium model is a line with an initial (y-intercept) value of 37, and a slope of 29.

The slope of a line is the ratio of change of the independent variable (potassium content) to the dependent variable (fiber content).

           $slope=\dfrac{\Delta potassium}{\Delta fiber}=\dfrac{29mg\text{ of potassium}}{1g\text{ of fiber}}$

Thus, that shows that the slope means the the model predicts the cereals will have approximately 29 more miligrams of potassium for every additional gram of fiber.