Chapter 8, Problem 50E

To determine

To explain would a model that uses the person’s waist size be able to predict the body fat more accurately than one that uses weight and create and analyze that model.

Answer to Problem 50E

Yes, a model that uses the person’s waist size is able to predict the body fat more accurately than one that uses weight. And the regression line is:

  $\text{\%<mover accent="true"><mo>B</mo><mo>^</mo></mover> ody fat}=-62.56+2.22(\text{Waist size)}$ .

Explanation of Solution

In the previous question, the %body fat and weight of the people is given as researcher wants to find out ways to make a good estimate to calculate the body fat. Thus, the table is given in which the body fat and their weights are given.

And the regression line is as:

  $\text{\%<mover accent="true"><mo>B</mo><mo>^</mo></mover> ody fat}=-27.4+0.25(\text{Weight)}$

Thus, we can say that a model that uses the person’s waist size is able to predict the body fat more accurately than one that uses weight because waist size seems to be more closely related to body fat percentage than weight. Thus, the regression line of the percentage body fat and waist size is calculated by using excel as:

We will first select the data given in the table and then go to the insert tab. In the tab we will use the scatterplot option from the charts options and then the scatterplot will appear on the screen. Now, we will go to the design tab from the chart tools. We will then select the quick layout option from it. Then in it we will select the layout $9$ from it and the scatterplot with the model and regression line will appear as:

  

Thus, the regression line to predict the body fat using waist size is as:

  $\begin{array}{l}\text{\%<mover accent="true"><mo>B</mo><mo>^</mo></mover> ody fat}=\alpha +\beta (\text{Waist size)}\\ =-62.56+2.22(\text{Waist size)}\end{array}$

Thus, the residual appear to be equally spread so a linear model is appropriate. Thus we can say that body fat percentage increases by about $2.22$ percentage per waist size.