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 potassium = 36 + 25fiber. explain what the slope means.
choose the correct answer below.
o a. the model predicts that cereals will have approximately 36 more milligrams of potassium for every additional gram of fiber.
o b. the model predicts that cereals will have approximately 25 more grams of fiber for every additional milligram of potassium.
o c. the model predicts that cereals will have approximately 36 more grams of fiber for every additional milligram of potassium.
o d. the model predicts that cereals will have approximately 25 more milligrams of potassium for every additional gram of fiber.

Explanation:

In a regression model \( y = a+bx\), \(b\) is the slope. Here, the regression model is \( Potassium = 36 + 25Fiber\). The slope is \(25\). The independent variable is \(Fiber\) (in grams) and the dependent variable is \(Potassium\) (in milligrams). The slope represents the change in the dependent variable for a unit change in the independent variable. So, for each additional gram of fiber (\(x\) increases by \(1\)), the amount of potassium (\(y\)) increases by \(25\) milligrams.

Answer:

D. The model predicts that cereals will have approximately 25 more milligrams of potassium for every additional gram of fiber.