ship_leg	speed	fuel
1	15	37
1	15.4	38
1	15.5	38
1	15.7	39
1	15.8	39
1	15.9	40
1	16	42
1	16.2	43
1	16.3	43
1	16.4	44
1	16.5	45
1	16.6	45
1	16.9	47
1	17	47
1	17.1	50
1	17.3	53
1	17.5	55
1	17.6	56
1	17.7	58
1	18	60
2	18.2	65
2	18.5	67
2	18.7	69
2	18.8	72
2	19	73
2	19.4	75
2	19.6	76
2	19.7	77
2	19.8	78
2	20	82
2	20.3	84
2	20.4	85
2	20.5	87
2	20.6	90
2	20.7	93
2	20.8	96
2	20.9	98
2	21.1	101
2	21.2	103
2	21.5	108
3	16.1	45
3	16.4	46
3	16.5	46
3	16.8	48
3	16.9	49
3	17	51
3	17	51
3	17	52
3	17.1	52
3	17.1	53
3	17.4	56
3	17.6	59
3	17.9	64
3	18.2	67
3	18.4	69
3	18.5	70
3	18.5	71
3	18.9	74
3	19	75
3	19.8	80
4	17	81
4	17.9	89
4	18.4	98
4	18.5	100
4	18.8	103
4	18.9	106
4	18.9	105
4	19	109
4	19.3	115
4	19.4	117
4	19.5	118
4	19.6	121
4	19.7	123
4	19.7	124
4	20.2	132
4	20.4	135
4	21	147
4	21.4	155
4	22	178
4	23	200
5	15.8	68
5	16.1	70
5	16.5	75
5	16.8	76
5	16.9	79
5	17	82
5	17	81
5	17.2	84
5	17.2	83
5	17.4	85
5	17.5	86
5	17.8	87
5	17.8	88
5	18	92
5	18	93
5	18.4	97
5	18.6	102
5	20.1	128
5	20.5	135
5	21	146

Engineering insights into a given ship's fuel consumption on a given route based on the vessel's speed gives the equation: fuel=A(speed)3 where A is some constant that depends on the vessel shape, the water conditions, etc. When looking over a long distance, however, the same speed is not maintained throughout the duration of the trip. To correct for this, engineers typically instead use the equation: totalfuel=Ai(averagespeed)bi

The constantsAi andbi are different for each vessel for each route.

A.

What is the predicted fuel consumption for a vessel traveling with an average speed of 25 on a route for which the vessel has the following values of A and b?

B.

There are 5 combinations of ship/route, referred to as ship_leg. They are numbered 1 through 5. Each ship_leg has a different value of A and b. Find the best estimates of A and b for each ship_leg by minimizing the sum of squared residuals.

What is the minimized sum of squared residuals?

Hint: to get the correct answer, you have to add up the squared residual for every row in the dataset.

C.

Using the values of A and b that minimize the sum of squared residuals, what is the predicted value of fuel consumption for ship_leg=1 in the case that the average speed is 19?