Question

the data set shown represents the total fee for miles traveled on a toll road. use the information to complete the statements. there are observed toll fee values. it costs $ to travel 76 miles. the predicted value for traveling 30 miles is $ linear regression y ≈ 0.043x + 0.324; r ≈ 0.992 -1 ≤ x ≤ 150 -1 ≤ y ≤ 10

Explanation:

Step1: Count data - points

The number of pairs of \(x\) (miles) and \(y\) (toll - fee) values in the data set is 6. So, the number of observed toll - fee values is 6.

Step2: Find cost for 76 miles

We are given the linear regression equation \(y = 0.043x+0.324\). Substitute \(x = 76\) into the equation: \(y=0.043\times76 + 0.324\).
\[

$$\begin{align*} y&=0.043\times76+0.324\\ &=3.268 + 0.324\\ &=3.592\approx3.59 \end{align*}$$

\]

Step3: Find predicted value for 30 miles

Substitute \(x = 30\) into the linear regression equation \(y = 0.043x+0.324\).
\[

$$\begin{align*} y&=0.043\times30+0.324\\ &=1.29+0.324\\ &=1.614\approx1.61 \end{align*}$$

\]

Answer:

There are 6 observed toll - fee values.
It costs $3.59 to travel 76 miles.
The predicted value for traveling 30 miles is $1.61.