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:

mpg^=36.993.864×Engine size\hat{\text{mpg}} = 36.99 - 3.864 \times \text{Engine size}

Given that the engine size is 4 liters:

mpg^=36.993.864×4\hat{\text{mpg}} = 36.99 - 3.864 \times 4

Now, calculating the result:

mpg^=36.9915.456=21.534\hat{\text{mpg}} = 36.99 - 15.456 = 21.534

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:

  1. What does the negative coefficient for engine size mean in this regression model?
  2. How would the mpg change if the engine size were 5 liters?
  3. What is the significance of the constant value 36.99 in this equation?
  4. How do you interpret the slope of -3.864 in practical terms?
  5. 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