Chapter 12 Assignment
Here are advertised horsepower ratings and expected gas mileage for several randomly selected 2010 vehicles.
Car horsepower Miles per gallon
Audi A4 210 30
BMW 3 series 240 29
Buick LaCrosse 150 26
Chevy Cobalt 140 37
Chevy Suburban 1500 330 21
Ford Expedition 300 18
GMC Yukon 310 19
Honda Civic 150 36
Honda Accord 187 31
Hyundai Elantra 148 35
Lexus IS 350 306 25
Lincoln Navigator 310 20
Mazda Tribune 171 28
Toyota Camry 169 33
Volkswagen Beetle 150 28
- Find the equation of the least-squares line: 𝑦̂ = 𝑎 + 𝑏𝑥. Round your results to two decimal places.
- Compute the coefficient of determination, 𝑟2 . What percentage of the variation in 𝑦 can be explained by the corresponding variation in 𝑥 (be sure to write this statement about miles per gallon and horsepower). What percentage is due to other factors? What does this tell you about how well our model fits the given data?3. Interpret the slope of your least-squares line in the context of this application (what does the specific numeric value of the slope mean in terms of the relationship between horsepower and miles per gallon?).
- Use a 5% level of significance to test the claim that 𝜌 < 0.
- State the null and alternative hypotheses.
- What calculator test will you use? List the requirements that must be met for you to use this test, and indicate whether the conditions are met in this problem.
- Run the calculator test and obtain the P-value.
- Based on your P-value, will you reject or fail to reject the null hypothesis?
- Interpret your conclusion from part d in the context of this problem. In other words, what does this result tell you about the population correlation between horsepower and gas mileage?