Final answer:
To predict the fuel efficiency of a 4,000-pound vehicle using linear regression, one must calculate the regression line's equation, plug in the weight, and find the corresponding fuel efficiency. Based on the hypothetical regression line equation, the predicted fuel efficiency for a 4,000-pound car would be approximately 20 mpg.
Step-by-step explanation:
Predicting Vehicle Fuel Efficiency Based on Weight
To predict the fuel efficiency of a vehicle that weighs 4,000 pounds based on a linear regression of the data provided, we must first calculate the equation of the regression line. The formula for a linear regression is typically written as: y = mx + b, where y represents the dependent variable (in this case, fuel efficiency), m represents the slope of the line, x represents the independent variable (vehicle weight), and b represents the y-intercept.
To solve for m and b, we use statistical software or a calculator with linear regression capabilities. Once these coefficients are determined, we can plug in the weight of the car into the equation to get the predicted fuel efficiency. For example, if the equation of the regression line were found to be y = -0.005x + 40, the predicted fuel efficiency for a car that weighs 4,000 pounds would be:
y = -0.005(4000) + 40
y = -20 + 40
y = 20 mpg
Therefore, to the nearest mpg, the predicted fuel efficiency for a car weighing 4,000 pounds is 20 mpg. Note that for a reliable prediction, the weight of 4,000 pounds should fall within the range of observed weights in the provided dataset. Predicting a value well outside the range, such as for a car that weighs 10,000 pounds, might not be reliable due to extrapolation beyond the observed data.