## Solution Library

# A Model to Explain the Variation in Fuel Efficiency using Regression Model

**Question**

Use the data in “auto-mpg.xlsx.” The dataset contains a sample of 100 cars. The variables include Displacement (in liters), Engine Power (in horsepower), and Weight (in tons), which are believed to be related to the Fuel Efficiency (miles per gallon).

- As an analytics consultant, you are expected to develop a model to explain the variation in Fuel Efficiency. You hypothesize the following model: Fuel Efficiency=β_0+β_1*Displacement+ β_2*Engine Power+ β_3*Weight+ ε
- Using Excel, construct a scatter plot for each of the following paired variables (three scatter plots total): Fuel Efficiency and Displacement, Fuel Efficiency and Engine Power, and Fuel Efficiency and Weight. Attach your scatter plots and interpret them – does each independent variable suggest a linear relationship with the dependent variable? If so, does it seem to be positive or negative?
- Using Excel, run a multiple linear regression to estimate the unknown parameters β_0, β_1, β_2, and β_3. Report your least squares prediction equation and attach your output from Excel.
- Is there sufficient evidence that the overall model is useful for predicting Fuel Efficiency? Test by conducting an F Test and use. Attach the portion of the output from Excel that is required to do this test.
- Does Fuel Efficiency decrease as the average Weight increases when the other independent variables are held constant? Test by conducting a hypothesis test for β_3 and use . Attach your output from Excel.
- Determine and interpret the value of R^2.
- Use the model developed in part b to estimate the Fuel Efficiency in miles per gallon when the Displacement is 0.4 liters, the Engine Power is 150 horsepower, and the Weight of the car is 1.75 tons.

**Summary**

This question belongs to econometrics and discusses about to develop a model to explain the variation in Fuel Efficiency using multiple linear regression model.

Total word count: 535

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