Chapter 4.5, Problem 7E

To determine

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

  $y=-1.3x+1$

  

Answer to Problem 7E

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

Explanation of Solution

Given:

  $y=-1.3x+1$

  

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 $y=-1.3x+1$	Residual
$-8$	$9$	$11.4$	$9-11.4=-2.4$
$-6$	$10$	$8.8$	$10-8.8=1.2$
$-4$	$5$	$6.2$	$5-6.2=-1.2$
$-2$	$8$	$3.6$	$8-3.6=4.4$
$0$	$-1$	$1$	$-1+1=0$
$2$	$1$	$-1.6$	$1+1.6=2.6$
$4$	$-4$	$-4.2$	$-4+4.2=0.2$
$6$	$-12$	$-6.8$	$-12+6.8=-5.2$
$8$	$-7$	$-9.4$	$-7+9.4=2.4$

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.