Problem 1
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 servings of 77 breakfast cereals produced the regression model Potassium \(=38+27\) Fiber. If your cereal provides 9 grams of fiber per serving, how much potassium does the model estimate you will get?
Problem 2
In Chapter 7 's Exercise 33 we examined the relationship between the fuel economy \((\mathrm{mpg})\) and horsepower for 15 models of cars. Further analysis produces the regression model \(\widehat{m p g}=46.87-0.084 H P\). If the car you are thinking of buying has a 200-horsepower engine, what does this model suggest your gas mileage would be?
Problem 3
Exercise 1 describes a regression model that estimates 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?
Problem 4
Exercise 2 describes a regression model that uses a car's horsepower to estimate its fuel economy. In this context, what does it mean to say that a certain car has a positive residual?
Problem 5
The regression model \(\widehat{\text { Potassium }}=38+27\) Fiber relates fiber (in grams) and potassium content (in milligrams) in servings of breakfast cereals. Explain what the slope means.
Problem 6
The regression model \(\widehat{m p g}=46.87-0.084 H P\) relates cars \(^{\prime}\) horsepower to their fuel economy (in mpg). Explain what the slope means.
Problem 7
The correlation between a cereal's fiber and potassium contents is \(r=0.903\). What fraction of the variability in potassium is accounted for by the amount of fiber that servings contain?
Problem 8
The correlation between a car's horsepower and its fuel economy (in mpg) is \(r=-0.869\). What fraction of the variability in fuel economy is accounted for by the horsepower?
Problem 13
If you create a regression model for predicting the Weight of a car (in pounds) from its Length (in feet), is the slope most likely to be \(3,30,300\), or 3000 ? Explain.
Problem 14
If you create a regression model for estimating the Height of a pine tree (in feet) based on the Circumference of its trunk (in inches), is the slope most likely to be \(0.1,1,10\), or \(100 ?\) Explain.
