Question

1. a study of the fuel economy for various automobiles plotted the fuel consumption (in gallons of gasoline used per 100 km traveled) vs. speed (in km per hour). a least - squares line was fitted to the data. here is the residual plot from this regression analysis. which statement is true? (a) the residual plot confirms the linearity of the relationship between speed and fuel consumption. (b) the correlation between speed and fuel consumption is negative until a speed of 50, then positive. (c) the linear relationship between fuel consumption and speed is strong and positive. (d) the residual plot indicates that the relationship between speed and fuel consumption is not linear. (e) the least - squares line should be used to predict fuel consumption from speed because the residual plot shows a strong curved pattern.

Explanation:

Step1: Understand residual plot concept

A residual plot shows the difference between observed and predicted values. If the relationship is linear, the residual plot should have a random scatter of points.

Step2: Analyze given residual plot

The given residual plot has a curved - like pattern. This indicates that the relationship between speed and fuel consumption is not linear. When the residual plot has a non - random pattern (like a curve), a linear model is not appropriate.

Step3: Evaluate each option

• Option A: A residual plot with a non - random pattern does not confirm linearity.
• Option B: The plot does not clearly show a consistent negative or positive correlation between speed and fuel consumption throughout.
• Option C: The plot does not suggest a linear relationship between speed and fuel consumption for all speeds.
• Option D: The residual plot indicates non - linearity, not linearity.
• Option E: Since the residual plot has a strong curved pattern, a least - squares line (which assumes linearity) should not be used to predict fuel consumption. This option is correct.

Answer:

E. The least - squares line should be used to predict fuel consumption from speed because the residual plot shows a strong curved pattern.