Question

A scatterplot was created using the miles per gallon and weight of 20 cars. What is the purpose of creating this scatterplot?

1) To analyze the relationship between miles per gallon and weight of cars
2) To calculate the average miles per gallon of the 20 cars
3) To determine the brand of the cars based on their weight
4) To compare the prices of the cars based on their weight

Answer 1

The scatterplot analyzing miles per gallon versus weight of cars is made to observe the relationship between fuel efficiency and weight. The slope of the least-squares line describes how efficiency changes with weight. Predictions using the line depend on if the weight in question fits within the range of the original dataset.

Step-by-step explanation:

The purpose of creating a scatterplot using the miles per gallon and weight of 20 cars is to analyze the relationship between the fuel efficiency and the weight of the cars. This type of visual representation allows researchers to determine if a pattern exists, such as a tendency for heavier cars to have lower fuel efficiency or vice versa. It is used to identify trends, correlations, and potential outliers in the data set.

The fuel efficiency, represented in miles per gallon, is typically considered the dependent variable because it is likely to depend on or change according to the car's weight, the independent variable. Plotting this data on a scatterplot and possibly fitting a least-squares line would provide a quantitative way to predict fuel efficiency based on a car's weight.

Practical Interpretation of Slope and Predictions

In terms of fuel efficiency and weight, the slope of the least-squares line indicates how fuel efficiency changes as a car's weight changes. In general, we would expect a negative slope, showing that as the weight increases, fuel efficiency tends to decrease. However, the practical interpretation depends on the actual slope from the analysis: a steeper negative slope would indicate a more pronounced effect of weight on fuel efficiency.

To predict fuel efficiency for a specific weight, you would use the equation of the least-squares line: if the line's equation were known, you could substitute 4,000 pounds into the equation to find the corresponding fuel efficiency in miles per gallon. Predicting fuel efficiency for a 10,000-pound vehicle may not be reasonable if such weights were not represented in the original data; the least-squares line makes predictions based on the range of data from which it was generated.