Chapter 4.5, Problem 5E

To determine

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

  $y=4x-5$

  

Answer to Problem 5E

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

Explanation of Solution

Given:

  $y=4x-5$

  

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 $y=4x-5$	Residual
$-4$	$-18$	$-21$	$-18+21=3$
$-3$	$-13$	$-17$	$-13+17=4$
$-2$	$-10$	$-13$	$-10+13=3$
$-1$	$-7$	$-9$	$-7+9=2$
$0$	$-2$	$-5$	$-2+5=3$
$1$	$0$	$-1$	$0+1=1$
$2$	$6$	$3$	$6-3=3$
$3$	$10$	$8$	$10-8=2$
$4$	$15$	$9$	$15-9=6$

Plotting the above points on the graph, we have:

  

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

Thus, the model is a good fit for the data in the table.

Conclusion:

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