Question

We are interested in predicting the fuel efficiency (gasoline mileage in mpg) using the weight of a vehicle in pounds. A random sample of 12 vehicles is taken. The Excel output is given below. Use the output and the fact that R² = 0.640 to answer the following questions.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	48.409	5.978	8.098	0.000	35.089	61.728
Weight	-0.006	0.002	-4.214	0.002	-0.010	-0.002

1. Interpret the slope in context.
2. Interpret the coefficient of determination in context.
3. For a 3500-pound vehicle, the Fuel efficiency is 22 mpg, find the residual.

Answer 1

1.

The coefficient of determination is 0.64

It tells us that 64 % change in the mileage of the vehicle happens due to change in weight of the vehicle. 64 % variation in mileage is explained by the weight of the vehicle. (the remaining 36 % change or variation is due to other factors that we have not considered under study for example, engine horsepower.)

Let y^ predicted fuel efficiency

Let X be the weight of vehicle

The predicted fuel efficiency is given by,

y^ = 48.409 - 0.006 * x

Hence, for x = 3500,

y^ = 48.409 - 0.006 * 3500

y ^ = 27.409

The residual is given by,

= Y - y^

Where Y is actual value of fuel efficiency

= 22 - 27.409 = - 5.409

The residual is, - 5.409