The fuel consortium chairman at an airport recorded the cost per barrel of crude oil and the cost per barrel of jet fuel each week. After plotting his results, the chairman noticed that the relationship between the two variables was fairly linear, so he used the data to calculate the following least squares regression equation for predicting the cost, in dollars, per barrel of jet fuel from the cost, in dollars, per barrel of crude oil.

y ^ = 2 + 6 / 7 x

What is the residual of a week in which a barrel of crude oil costs $60 and a barrel of jet fuel costs $78?

residual cost = $24.57

Step-by-step explanation:

The residual is the difference between the observed value of y and the predicted value of y. The least square regression equation was used to predict cost in dollars per barrel of jet fuel from the cost, in dollars, per barrel of crude oil. The residual value is the difference between the observed or measured value and the predicted value of the regression model. The predicted value is gotten from the regression equation.

y = 2 + 6/7 x

where

x = cost of a barrel of crude oil

x = $60

y = 2 + 6/7 * 60

y = 2 + 360/7

y = 2 + 51.4285714286

y = 53.4285714286

y = $53. 43

predicted cost = $53. 43

Measured cost = $78

residual = observed value - predicted value

residual = 78 - 53.43

residual cost = $24.57