91Ó°ÊÓ

$\begin{array}{|ll|}\hline \text{Distance}& \text{Height}\\ 1500& 1000\\ 1340& 828\\ 1328& 800\\ 1172& 600\\ 800& 300\\ \hline\end{array}$

The scatterplot is swinging higher, hence the direction is positive.

Because there is no straight line connecting the ends, the form is curved.

Because all spots in the same pattern are so close together, the strength is solid.

$\begin{array}{|ll|}\hline \text{Distance}& \text{Height}\\ 1500& 1000\\ 1340& 828\\ 1328& 800\\ 1172& 600\\ 800& 300\\ \hline\end{array}$

Exponential Model

Power Model

The height logarithm is in the horizontal dimension in the Exponential Model, the distance logarithm is in the y axis in the Power Model, and the height logarithm is in the horizontal axis in the Power Model.

The Power Model is used to model the relationship between the variables, with the most linear version shown in the accompanying scatterplot.

$\begin{array}{|ll|}\hline \text{Distance}& \text{Height}\\ 1500& 1000\\ 1340& 828\\ 1328& 800\\ 1172& 600\\ 800& 300\\ \hline\end{array}$

The height and distance values are logarithmic.

$\begin{array}{|llll|}\hline \text{Height}\left(X\right)& \text{Distance}\left(Y\right)& XY& XX\\ 6.907755& 7.31322& 50.517932& 47.71708\\ 6.719013& 7.200425& 48.379749& 45.14514\\ 6.684612& 7.191429& 48.071913& 44.68404\\ 6.39693& 7.066467& 45.203695& 40.92071\\ 5.703782& 6.684612& 38.12757& 32.53313\\ ∑X=32.412092& ∑Y=35.456153& ∑XY=230.30086& ∑X^2=211.0001\\ \hline\end{array}$

$a=\frac{∑Y·∑X^2-∑X·∑XY}{n∑X^2-{\left(∑X\right)}^2}=3.751$

$b=\frac{n∑XY-∑X.∑Y}{n∑X^2-{\left(∑X\right)}^2}=0.515$

$y=a+bx$

role="math" localid="1652861160820" $y=3.751+0.515x$

The equation from part(c)

$y=3.751+0.515x$

Using the value of $x=700$in the component equation (c)

$$\begin{gathered} \text{ln}\hat{y}=3.751+0.515\ln \left(700\right) \\ =7.12481 \end{gathered}$$

Now we take the Exponential of the above equation

$$\begin{gathered} \hat{\mathit{y}}=e^{7.12481} \\ =1242.41 \end{gathered}$$