Chapter 4.5, Problem 6E

To determine

To determine whether the model is a good fit for the data in the table −

  $y=6x+4$

  

Answer to Problem 6E

The model isa good fit for the data in the table.

Explanation of Solution

Given:

  $y=6x+4$

  

Formula Used:

A residual is a measure of how well a line fits an individual data point. This vertical distance is known as a residual. For data points above the line, the residual is positive, and for data points below the line, the residual is negative. The closer a data point's residual is to $0$ , the better the fit.

Calculation:

$x$	$y$	$y$ value from the model $y=6x+4$	Residual
$1$	$13$	$10$	$13-10=3$
$2$	$14$	$16$	$-13+17=4$
$3$	$23$	$22$	$23-22=1$
$4$	$26$	$28$	$26-28=-2$
$5$	$31$	$34$	$31-34=-3$
$6$	$42$	$40$	$42-40=2$
$7$	$45$	$46$	$45-46=-1$
$8$	$52$	$52$	$52-52=0$
$9$	$62$	$58$	$62-58=4$

Plotting the above points on the graph, we have:

  

From the above graph, we can see that the residuals form a straight line.

Thus, the model isa good fit for the data in the table.

Conclusion:

The model is a good fit for the data in the table.