Chapter 4, Problem 11CR

To determine

To find: The equation that models the roasting time as a function of the weight of the turkey. Then, interpret the slope and the y intercept of the line of fit.

Answer to Problem 11CR

The required model for the roasting time is $y=\frac{2.5}{12}x+\frac{4}{3}$ . The y intercept of the line of the best fit has no meaning as the roasting time cannot be zero when the weight of the turkey is 0.

Explanation of Solution

Given:

The given scatter plot is shown in Figure 1.

Figure 1

Calculation:

The scatter plot for the given data set is shown in Figure 2

Figure 2

From the above plot use any two points to calculate the slope of the line as consider the slope with the points $\left(8,3\right),\left(20,5.5\right)$ ,

  $\begin{array}{c}m=\frac{5.5-3}{20-8}\\ =\frac{2.5}{12}\end{array}$

Then, the equation of the line passing through the point $\left(8,3\right)$ is obtained as,

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-3=\frac{2.5}{12}\left(x-8\right)\\ y=\frac{2.5}{12}x+\frac{4}{3}\end{array}$

Thus, the required model for the roasting time is $y=\frac{2.5}{12}x+\frac{4}{3}$ .

The y intercept of the line of the best fit has no meaning as the roasting time cannot be zero when the weight of the turkey is 0.