Answer:
Residual for the week will be $6.
Step-by-step explanation:
Regression equation predicting the per barrel cost of jet fuel is,
[tex]\hat{y}=2+\frac{7}{6}x[/tex]
where, [tex]\hat{y}[/tex] = cost of jet fuel
x = cost of crude oil per week
If the cost of crude oil in any week = $60
Then predicted cost of jet fuel,
[tex]\hat{y}=2+[\frac{7}{6}\times (60)][/tex]
= 2 + 70
= $72
Residual price = Actual cost - predicted cost
= $78 - $72
= $6
Therefore, residual price will be $6.
The residual of the week in which a barrel of crude oil costs $60 is $6
The least square regression equation is given as:
[tex]\mathbf{\^y = 2 + \frac 76x}[/tex]
When a barrel of crude oil costs $60, it means that x = 60.
So, we have:
[tex]\mathbf{\^y = 2 + \frac 76 \times 60}[/tex]
[tex]\mathbf{\^y = 2 + 7 \times 10}[/tex]
Multiply
[tex]\mathbf{\^y = 2 + 70}[/tex]
Add
[tex]\mathbf{\^y = 72}[/tex]
So, we have:
Actual Cost = $78
Predicted Cost = $72
The residual is then calculated as:
[tex]\mathbf{Residual = Actual - Predicted }[/tex]
This gives
[tex]\mathbf{Residual = \$78 - \$72}[/tex]
Subtract
[tex]\mathbf{Residual = \$6}[/tex]
Hence, the residual of the week is $6
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