Chapter 4, Problem 9CA

a.

To determine

To select: The points that appear on the scatter plot of the residuals.

Answer to Problem 9CA

The points that appear on scatter plot of the residuals are $(92,-6),(78,96),(60,-10),(84,58),(98,-64),(72,94),(54,-72),(68,26).$

Explanation of Solution

Given Information: Table showing the values of daily high temperatures $x$ and the numbers $y$ of frozen fruit bars sold on eight days is given. Equation modeling the data is $y=3x-50$ .

Calculation:

Using given data values and model, calculating the residuals and arranging the results in a table,

  $\begin{array}{l}\begin{array}{llll}x\hfill & y\hfill & y(from\mathrm{mod}el)\hfill & \mathrm{Re}sidual\hfill \\ 54\hfill & 40\hfill & 112\hfill & -72\hfill \\ 60\hfill & 120\hfill & 130\hfill & -10\hfill \\ 68\hfill & 180\hfill & 154\hfill & 26\hfill \\ 72\hfill & 260\hfill & 166\hfill & 94\hfill \\ 78\hfill & 280\hfill & 184\hfill & 96\hfill \\ 84\hfill & 260\hfill & 202\hfill & 58\hfill \\ 92\hfill & 220\hfill & 226\hfill & -6\hfill \\ 98\hfill & 180\hfill & 244\hfill & -64\hfill \end{array}\end{array}$

The scatter plot of the residuals is:

  

The points that appear on scatter plot of the residuals are $(92,-6),(78,96),(60,-10),(84,58),(98,-64),(72,94),(54,-72),(68,26).$

b.

To determine

Whether the model is a good fit for the data.

Answer to Problem 9CA

The equation $y=3x-50$ is not a good fit for the data.

Explanation of Solution

Given Information: Table showing the values of daily high temperatures $x$ and the numbers $y$ of frozen fruit bars sold on eight days is given. Equation modeling the data is $y=3x-50$ and calculations from previous part.

The points are not evenly dispersed about the horizontal axis. Therefore, the equation $y=3x-50$ is not a good fit for the data.