Exercise 17 Page 224

Let's use the calculator to draw a scatter plot of the data. Push the $\boxed{\text{STAT}}$ button, choose Edit, and enter your values.

Once the values have been entered we can plot them by pushing $\boxed{2\text{nd}},$ $\boxed{\text{Y=}},$ and then choosing one of the plots in the list. Make sure you turn the plot ON before you choose the scatter plot type. Then, match the lists for the $x\text{-}$ and $y\text{-}$values accordingly.

By pushing $\boxed{\text{GRAPH}}$ the calculator will plot the data. Note that we will need to change the viewing window so that we can see all of the points.

We can see an increasing trend with a bit of a curve at the start and at the end, so let's use a cubic regression. We can access this option by pressing the $\boxed{\text{STAT}}$ button and choosing CubicReg from the CALC menu. After matching the lists for the $x\text{-}$ and $y\text{-}$values and setting the place to store the equation, move to the last line and press $\boxed{\text{ENTER}}.$

The result screen gives the coefficients of the cubic model. Since the regression equation is now stored in the memory of the calculator, when we press $\boxed{\text{GRAPH}}$ again we can see the regression line with the scatter plot.

We can use the calculator to estimate the average speed of the pontoon boat when the engine speed is $2800$ RPM. Push $\boxed{\text{2nd}}$ and $\boxed{\text{TRACE}},$ choose value from the menu, and set $x=28.$ Note that we need to use $28$ and not $2800,$ since the data is given using hundreds of revolutions per minute.

We can also check this result by substituting $x=28$ in the regression equation. We can see that the calculated value and the value the calculator gives are approximately the same. The reason for the difference is that we used rounded values for the coefficients. The estimated speed of the pontoon boat when the engine speed is $2800$ RPM is $16.1$ miles per hour.