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? y = 0.035x - 13.989, y = 0.035x + 13.989, y = -0.035x + 13.989, y = -0.035x - 13.989

Explanation:

Step1: Recall linear - regression formula

The general form of a simple linear - regression equation is $y = mx + b$, where $y$ is the dependent variable, $x$ is the independent variable, $m$ is the slope, and $b$ is the y - intercept. In the context of the problem, the number of gallons in the tank ($y$) is the dependent variable and the number of miles driven ($x$) is the independent variable. As the number of miles driven increases, the number of gallons in the tank decreases, so the slope $m$ should be negative.

Step2: Analyze the options

We are looking for an equation of the form $y=mx + b$ where $m<0$. Among the given options $y = 0.035x-13.989$, $y = 0.035x + 13.989$, $y=-0.035x + 13.989$, and $y=-0.035x-13.989$, the correct form considering the physical situation (more miles driven means less gas in the tank) is $y=-0.035x + 13.989$. The negative slope indicates that as $x$ (miles driven) increases, $y$ (gallons in the tank) decreases, and the positive y - intercept of 13.989 represents the initial amount of gas in the tank (when $x = 0$).

Answer:

$y=-0.035x + 13.989$