Chapter 4, Problem 9CA

(a)

To determine

To select: The points that appear on a scatter plot of the residuals

Answer to Problem 9CA

Points appear on a scatter plot of the residuals are

  $(98,-64),(72,94),(54,-72)and(68,26)$

Explanation of Solution

Given:

Temperature $(F),x$	$54$	$60$	$68$	$72$	$78$	$84$	$92$	$98$
Frozen fruit bars, $y$	$40$	$120$	$180$	$260$	$280$	$260$	$220$	$180$

Calculation:

Consider the table shows the daily high temperatures $(F),x$ and the numbers $y$ of frozen fruit bars sold on eight randomly selected days. The equation $y=3x-50$ models the data

First, find the residuals

$x$	$y$	$y$ Value from model	Residual
$54$	$40$	$112$	$40-112=-72$
$60$	$120$	$130$	$120-130=-10$
$68$	$180$	$154$	$180-154=26$
$72$	$260$	$166$	$260-166=94$
$78$	$280$	$184$	$280-184=96$
$84$	$260$	$202$	$260-202=58$
$92$	$220$	$226$	$220-226=-6$
$98$	$180$	$244$	$180-244=-64$

Now make a scatter plot for residuals

  

Conclusion:

Points appear on a scatter plot of the residuals are

  $(98,-64),(72,94),(54,-72)and(68,26)$

(b)

To determine

whether the model is good fit for the data or not

Answer to Problem 9CA

The equation $y=3x-50$ does not fit for the data

Explanation of Solution

Given:

Temperature $(F),x$	$54$	$60$	$68$	$72$	$78$	$84$	$92$	$98$
Frozen fruit bars, $y$	$40$	$120$	$180$	$260$	$280$	$260$	$220$	$180$

Calculation:

The residual points form a $\cap$ shaped pattern, which suggests the data are not linear

The equation $y=3x-50$ does not fit for the data

Conclusion:

Therefore, the equation $y=3x-50$ does not fit for the data