Chapter 4.5, Problem 8E

To determine

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

  $y=-0.5x-2$

  

Answer to Problem 8E

The model is not a good fit for the data in the table.

Explanation of Solution

Given:

  $y=-0.5x-2$

  

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 $y=-0.5x-2$	Residual
$4$	$-1$	$2$	$-1-2=-3$
$6$	$-3$	$1$	$-3-1=-4$
$8$	$-6$	$0$	$-6-0=-6$
$10$	$-8$	$-1$	$-8+1=-7$
$12$	$-10$	$-2$	$-10+2=-8$
$14$	$-10$	$-3$	$-10+3=-7$
$16$	$-10$	$-4$	$-10+4=-6$
$18$	$-9$	$-5$	$-9+5=-4$
$20$	$-9$	$-6$	$-9+6=-3$

Plotting the above points on the graph, we have:

  

From the above graph, we can see that the residuals do not form a straight line.

Thus, the model is not a good fit for the data in the table.

Conclusion:

The model is not a good fit for the data in the table.