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University of South Florida *
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2321
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Industrial Engineering
Date
Apr 3, 2024
Type
docx
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2
Uploaded by BailiffLorisPerson840
Regional Rent-A-Car is interested in studying how weight of a vehicle is related to the fuel efficiency for several of its rental vehicles.
A random sample of 13 vehicles from Regional Rent-A-Car yielded the data in the table.
Weight (in pounds)
Fuel Efficiency (in miles per gallon)
2000
32.7
3123
22.8
3775
18.6
2287
26.1
4000
18.4
2485
26.2
2114
33.1
2433
28.3
2525
26.2
2889
22.5
3186
20.9
3258
21.3
3622
18.1
Part A
: Identify and interpret in context the estimate of the slope for the least-squares regression line. (5 points)
Sum of weight (x)= 37,697 Mean of x= 2,899.7692
Sum of miles per gallon (y)= 315.2 Mean of y= 24.2462
SS of x: 5091222.3077
SS of y: 306.212
SP: -37264.3615
Y=bx+b
Bx= sp/ssx = -37264.3615/5091222.3077= -0.007319
B= 24.2462-0.00732(2,899.7692) = 45.47054
Y= -0.073x+45.5 The fuel efficiency decreases 0.0073 for every pound increased.
Part B
: Identify and interpret in context the correlation coefficient. (5 points)
R= SP/((SS of x)(SS of y))= -37264.3615/ ((5091222.3077)(306.212))= -0.9438 This shows a strong negative correlation between weight and fuel efficiency.
Part C
: A car weighing 2,684 pounds had an average fuel efficiency of 24.6 miles per gallon. What is this car’s residual? (5 points)
-0.007319(2,684) +45.47=25.83
Part D
: Estimate the weight of a vehicle whose fuel efficiency is 20.2 miles per gallon. (5 points)
20.2= −0.07319x+45.47
X= 3,452.66
Part E
: Is this model the best fit for the data? Explain your reasoning. If a transformation is required, what is the equation for the new model? Show your work. (5 points)
No.
-0.007319x+ 45.47
Part F
: Using the transformation you gave in Part E, what would be the new estimate for fuel efficiency of the vehicle weighing 2,684 pounds? What effect did this new model have on the residual, compared to the result you found in Part C? Show all work. (5 points)
-0.00732 (2,684) +45.5 =25.86
25.86- 24.6= 1.26
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