Final answer:
The research examines the relationship between car weight and fuel efficiency using linear regression. A significant moderate negative correlation exists, indicating that heavier cars tend to have lower MPG. The analysis aids manufacturers and consumers in understanding how the weight of a vehicle impacts its fuel efficiency.
Step-by-step explanation:
The relationship between car weight and fuel efficiency (CityMPG) can be explored using linear regression analysis to address the research question: 'Is there a significant predictive relationship between the weight of a car and its miles per gallon (MPG) in the city among all cars on the road in Illinois in 2020?'
The null hypothesis (H0) would be that there is no relationship between car weight and CityMPG, whereas the alternative hypothesis (H1) would assert that there is a significant relationship between these two variables.
To interpret the slope of the regression line, we state that for each additional pound of car weight, the fuel efficiency in CityMPG changes by the slope value. The slope indicates the rate of change in fuel efficiency for each unit increase in car weight. For instance, if the slope is -0.01, it implies that for every additional 1,000 pounds, the car's fuel efficiency would decrease by 10 MPG.
A regression equation is used for prediction, such as for a 4,000-pound car. However, using this regression model to predict the MPG of a 10,000-pound car could be inappropriate if 10,000 pounds is outside the range of the weights in the dataset used to create the model, as it would involve extrapolation beyond the observed data.
The correlation coefficient of -0.56 suggests a moderate negative relationship between car weight and fuel efficiency, meaning heavier cars tend to have lower MPG. The coefficient of determination, calculated as (0.56)^2, reveals that approximately 31.36% of the variation in fuel efficiency can be explained by the car's weight.
Practical Significance of the Regression Analysis
This analysis is practical for car manufacturers and consumers alike, as it provides insights into how the weight of a vehicle affects its fuel efficiency, which can influence design, manufacturing decisions, and purchasing choices.