Exercise 12 Page 196

We have been given a table with data for $x$ and $y.$

$x$	$\text{-}4$	$\text{-}2$	$0$	$2$	$4$	$6$	$8$	$10$
$y$	$17$	$7$	$8$	$1$	$5$	$\text{-}2$	$2$	$\text{-}8$

In order to find a line of fit using our calculator, we need to first enter the values. Let's press the $\boxed{\text{STAT}}$ button.

Then we choose the first option in the menu, Edit, and fill in the values in lists L1 and L2.

We can perform a regression analysis on the data by pressing the $\boxed{\text{STAT}}$ button again, followed by using the right-arrow key to select the CALC menu.

This menu lists the various regressions that are available. If we choose the fourth option in the menu LinReg(ax+b) and press $\boxed{\text{ENTER}},$ the calculator performs a linear regression using the data that was entered.

We can round the values of $a$ and $b$ and substitute them into the equation $y=ax+b.$ This gives us the equation for the line of best fit. We can see how the line fits with the data by plotting the data points and graphing the line on the same coordinate plane. The calculator output gives us the value of the correlation coefficient, $r.$ This tells us that correlation is both negative and strong. We can tell that it is strong because it is close to $\text{-}1,$ which would be a direct correlation explained by a line that goes through all of the points.