Chapter 4.5, Problem 6E

To determine

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

Answer to Problem 6E

The model is 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 $y=6x+4$ .

Calculation:

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

  $\begin{array}{l}\begin{array}{llll}x\hfill & y\hfill & y(\mathrm{mod}el)\hfill & \mathrm{Re}siduals\hfill \\ 1\hfill & 13\hfill & 10\hfill & 3\hfill \\ 2\hfill & 14\hfill & 16\hfill & -2\hfill \\ 3\hfill & 23\hfill & 22\hfill & 1\hfill \\ 4\hfill & 26\hfill & 28\hfill & -2\hfill \\ 5\hfill & 31\hfill & 34\hfill & -3\hfill \\ 6\hfill & 42\hfill & 40\hfill & 2\hfill \\ 7\hfill & 45\hfill & 46\hfill & -1\hfill \\ 8\hfill & 52\hfill & 52\hfill & 0\hfill \\ 9\hfill & 62\hfill & 58\hfill & 4\hfill \end{array}\\ \end{array}$

Graph:

Making the scatter plot from the data,

  

Interpretation: As points are evenly distributed above and below the horizontal axis and residuals would sum to a number near about $0$ , the equation $y=6x+4$ models the data values fairly accurately.

Thus, the model is a good fit for the data values.