The Main Factors - Influencing the Fuel Consumption - Statistics Assignment Help

Assignment Task:

marks In order to determine the main factors, influencing the fuel consumption, a company collected data of 71 cars with the following set of variables:

• consumption — fuel consumption in litres per 100 km;
• weight — the weight of the car in 1000 pounds;
• transmission — the type of transmission (auto or manual);
• engine shape — either V-shaped or straight;
• gears — number of forwarding gears;
• quarter seconds — how many seconds it takes to get to a quarter of a mile;
• engine volume — the volume of an engine in litres;
• cylinders — number of cylinders in the engine;
• horsepower — a gross horsepower of the engine;
• secOto60 — how many seconds it takes to get from 0 to 60 mph.

The company thinks that all these variables are important, and they want to either confirm or disprove this hypothesis. They are also interested in a few insights about fuel consumption for some specific cars.

You will need to do the following steps in order to help the company:

1. Undertake a careful preliminary analysis of the data. Describe the relationships that you find, their possible causes and their practical implications. Explain how you could incorporate these into a regression model, including variables transformations that you think might be suitable.

2. Propose and construct at least two regression models (e.g. with different sets of explanatory variables and / or with different meaningful transformations of some of the variables) and select the best of them. Justify your choice. Your justification should include a full diagnostic analysis of your selected regression model, making sure that it does not violate the regression assumptions. If it does, then make adjustments in order to improve its quality, or explain why the violation of assumptions is not critical.
3. Using your preferred model, answer the following questions of the company:

• How does the weight of a car influence its fuel consumption? Give an interpretation of the relevant parameter(s) in the model.
• Does engine volume influence the fuel consumption? Justify your answer. If yes, what is the expected effect of the increase of the engine volume on the consumption?
• What would be the expected fuel consumption for a car that weighs 6,352 pounds, has a manual transmission, V-shaped engine of 8.3 litres, 6 gears, 8 cylinders, a horsepower of 444 and that gets to 60 mph in 12.7 seconds and does a quarter of a mile in approximately 20 seconds?
•  What would be the lowest and the highest values of fuel consumption for the car described in (c) in 95% of the cases?
•  What is the 90% confidence interval for the mean in the case of (c)?

 
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