Chapter 4.5, Problem 10E

To determine

If the model fits the given data in the table accurately.

Answer to Problem 10E

The model is not a good fit for the data values.

Explanation of Solution

Given information: Table of data containing values of $x$ and $y$ is given and equation of model is $y=1.3x+27$ .

Calculation:

Calculating the residuals using the model and given data and arranging the results in a table,

  $\begin{array}{llll}x\hfill & y\hfill & y(\mathrm{mod}el)\hfill & \mathrm{Re}sidual\hfill \\ 1\hfill & 27\hfill & 28.3\hfill & -1.3\hfill \\ 2\hfill & 28\hfill & 29.6\hfill & -1.6\hfill \\ 3\hfill & 36\hfill & 30.9\hfill & 5.1\hfill \\ 4\hfill & 28\hfill & 32.2\hfill & -4.2\hfill \\ 5\hfill & 32\hfill & 33.5\hfill & -1.5\hfill \\ 6\hfill & 35\hfill & 34.8\hfill & 0.2\hfill \end{array}$

Graph:

Making the scatter plot from the data,

  

Interpretation: As points are not evenly dispersed about the horizontal axis and residuals would not sum to a number near about $0$ . The equation $y=1.3x+27$ models the data values inaccurately.

Thus, the model is not a good fit for the data values.