Question

"Electric vehicles have become more popular in recent years due in part to advances in battery technology. How does full battery charge time relate to the driving range of the vehicle on a highway? The scatterplot and regression equation display this relationship for one specific electric vehicle from the current year. The equation of the regression line is ŷ=36.62 + 24.805x. Note that driving range varies with battery charge time, speed on the highway, and a number of other factors.

Calculate and interpret the residual for a vehicle that takes 8 hours to charge and has a highway range of 125 miles"

Answer 1

The residual for a vehicle that takes 8 hours to charge and has an actual highway range of 125 miles is -110.06 miles, indicating the actual range is less than the predicted range based on the regression equation ŷ=36.62 + 24.805x.

Step-by-step explanation:

You've asked how full battery charge time relates to the driving range of an electric vehicle and how to calculate the residual for a specific scenario. Given the regression equation ŷ=36.62 + 24.805x, we can predict the highway range (in miles) based on the battery charge time (x, in hours).

For a vehicle that takes 8 hours to charge (x=8), the predicted highway range would be:

ŷ = 36.62 + 24.805(8) = 36.62 + 198.44 = 235.06 miles

The actual highway range of the vehicle is 125 miles. To find the residual, which is the difference between the actual and predicted values, we subtract:

Residual = Actual - Predicted = 125 - 235.06 = -110.06 miles

The negative residual indicates that the actual highway range is 110.06 miles less than the predicted range for a vehicle that takes 8 hours to charge.