Question

the fare charged for a rideshare service is a function of the distance traveled. however, the fare differs according to the time of day, availability, and other variables. the distance and fares for 10 rides are shown in the table. the equation of the least - squares regression line is \\( \hat { y } = 5.21 + 2.33 x \\), where \\( \hat { y } \\) is the predicted fare and \\( x \\) is the distance. what is the residual for the rideshare cost with a distance of 5 miles? - 0.34 0.34 2.33 5.21

Explanation:

Step1: Calculate the predicted fare

Use the regression line formula $\hat{y}=5.21 + 2.33x$. Substitute $x = 5$ into the formula:
$$\hat{y}=5.21+2.33\times5=5.21 + 11.65=16.86$$

Step2: Calculate the residual

The formula for residual is $e=y-\hat{y}$. From the table, when $x = 5$, $y = 16.52$.
$$e=16.52 - 16.86=- 0.34$$

Answer:

-0.34