Chapter 4.5, Problem 10E

To determine

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

  $y=1.3x+27$

  

Answer to Problem 10E

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

Explanation of Solution

Given:

  $y=1.3x+27$

  

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 $y=1.3x+27$	Residual
$1$	$27$	$28.3$	$27-28.3=-1.3$
$2$	$28$	$29.6$	$28-29.6=-1.6$
$3$	$36$	$30.9$	$36-30.9=5.1$
$4$	$28$	$32.2$	$28-32.2=-4.2$
$5$	$32$	$33.5$	$32-33.5=-1.5$
$6$	$35$	$34.8$	$35-34.8=0.8$

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 nota good fit for the data in the table.

Conclusion:

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