Question

janelle tracks the number of miles she drives and the number of gallons of gas she has left. what is the linear regression model for this scenario? coefficient? the model? y = - 0.035x - 13.989 y = - 0.035x + 13.989 y = 0.035x + 13.989 y = 0.035x - 13.989

Explanation:

Step1: Analyze the relationship between miles driven and gallons in tank

As miles driven (\(x\)) increases, gallons in tank (\(y\)) decreases. So the slope \(m\) of the linear regression model \(y = mx + b\) should be negative.

Step2: Check the options for the correct form

Among the options \(y=-0.035x - 13.989\), \(y=-0.035x + 13.989\), \(y = 0.035x+13.989\), \(y=0.035x - 13.989\), when \(x = 0\) (no miles driven), the number of gallons should be a positive value.
For \(y=-0.035x + 13.989\), when \(x = 0\), \(y=13.989\) (a reasonable positive amount of gas in the tank initially). For \(y=-0.035x - 13.989\), when \(x = 0\), \(y=- 13.989\) (negative gallons is not possible).

Answer:

\(y=-0.035x + 13.989\)