Chapter 3.4, Problem 2AYU

To determine

To find: the line of best fitusing a graphing utility

Answer to Problem 2AYU

Using a graphing utility, the line of best fit is $y=1.7826+4.065x$

Explanation of Solution

Given:

$x$	$y$	$\left(x,y\right)$
$3$	$10$	$\left(3,10\right)$
$5$	$13$	$\left(5,13\right)$
$5$	$12$	$\left(5,12\right)$
$6$	$15$	$\left(6,15\right)$
$7$	$16$	$\left(7,16\right)$
$8$	$19$	$\left(8,19\right)$

Calculation:

Draw the scatter diagram by using graphing calculator.

Use the following operation to make the table.

Press STAT and ENTER (or $1$ ) to enter Stat Edit mode

The display is as shown below.

  

enter the $x$ values in first column, and corresponding $y$ values in second column.

Enter the values from the first column in $L_1$

Enter the $x$ values in $L_1$

Type $3$ ENTER , $5$ ENTER, $5$ ENTER etc.

Next enter the values from the second column $L_2$

Press to get into $L_2$ , and then press $10$ ENTER, $13$ ENTER etc.

The display is as shown below.

  

Now,

Press $2$ $Y=$ and set plot on

Press the ZOOM key and choose $9$ .

The display is as shown below.

The scatter diagram is as shown below.

  

Let the point $\left(3,10\right)and\left(8,19\right)$

Then the equation between these two points is,

  $y-y_1=m\left(x-x_1\right)$ Where these two points is,

  $y-10=\frac{19-10}{8-3}\left(x-3\right)$ Substitute the value of $x{1}_{},y_1,x_2,y_2$

  $\begin{array}{l}y-10=\frac{9}{5}\left(x-3\right)\\ 5\left(y-10\right)=9\left(x-3\right)\end{array}$ Multiply with $5$ on both sides.

  $\begin{array}{l}5y-50=9x-27\\ 5y=9x+23\end{array}$ Add $50$ on both sides

  $y=\frac{9}{5}x+\frac{23}{5}$

Sketch the graph of the line $y=\frac{9}{5}x+\frac{23}{5}$ by using graphing calculator.

Press $Y=$ and type the equation and then press GRAPH key.

The graph is as shown below.

  

Graphing utilities contain built in programs that find the line of best fit for a collection of points in a scatter diagram.

Press the STAT key and choose CALC $4$ .

The display is as shown below.

  

To find the line of best fit,

Press ENTER to produce the regression results shown in below figure.

The display is as shown below.

  

Using a graphing utility, the line of best fit is $y=1.7826+4.065x$

Conclusion:

Hence, the line of best fit is $y=1.7826+4.065x$