Math Problem Statement
Analysis of the relationship between the fuel economy (mpg) and engine size (liters) for 35 models of cars produces the regression model ModifyingAbove mpg with caret equals 36.99 minus 3.864 times Engine sizempg=36.99−3.864•Engine size. If a car has a 44 liter engine, what does this model suggest the gas mileage would be
Solution
To predict the gas mileage (in miles per gallon, mpg) for a car with a 4-liter engine using the regression model, you substitute the engine size (in liters) into the equation:
Given that the engine size is 4 liters:
Now, calculating the result:
So, the model suggests that the gas mileage for a car with a 4-liter engine would be approximately 21.53 mpg.
Would you like further details on the interpretation of this regression model, or have any additional questions?
Here are some related questions:
- What does the negative coefficient for engine size mean in this regression model?
- How would the mpg change if the engine size were 5 liters?
- What is the significance of the constant value 36.99 in this equation?
- How do you interpret the slope of -3.864 in practical terms?
- How would you assess the accuracy or fit of this regression model?
Tip: Always double-check the units for variables in a regression model to ensure you're interpreting results correctly. In this case, engine size is in liters, and mpg is the predicted outcome.
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Math Problem Analysis
Mathematical Concepts
Linear Regression
Algebra
Prediction Models
Formulas
\hat{\text{mpg}} = 36.99 - 3.864 \times \text{Engine size}
Theorems
Simple Linear Regression Theorem
Suitable Grade Level
Grades 10-12
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