Questions: The fuel efficiency (measured by miles per gallon) and the weight (in pounds) for a sample of vehicles were recorded and graphed in the scatterplot below. Which of the following is the most reasonable estimate of the correlation between these two variables? Hint: there is no calculation involved here. Use what you know about the properties of correlation. (A) 0.01 (B) 0.88 (C) -0.95 (D) -0.50 (E) 0.25

The fuel efficiency (measured by miles per gallon) and the weight (in pounds) for a sample of vehicles were recorded and graphed in the scatterplot below. Which of the following is the most reasonable estimate of the correlation between these two variables? Hint: there is no calculation involved here. Use what you know about the properties of correlation. (A) 0.01 (B) 0.88 (C) -0.95 (D) -0.50 (E) 0.25
Transcript text: The fuel efficiency (measured by miles per gallon) and the weight (in pounds) for a sample of vehicles were recorded and graphed in the scatterplot below. Which of the following is the most reasonable estimate of the correlation between these two variables? Hint: there is no calculation involved here. Use what you know about the properties of correlation. (A) 0.01 (B) 0.88 (C) -0.95 (D) -0.50 (E) 0.25
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Solution

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Solution Steps

Step 1: Analyzing the Scatterplot

The scatterplot shows a clear negative trend. As the weight of the vehicle increases, the fuel efficiency (miles per gallon) tends to decrease. This indicates a negative correlation. The points are also relatively close to forming a straight line, suggesting a strong correlation.

Step 2: Eliminating Positive Correlation Options

Because of the negative trend, we can eliminate options A (0.01), B (0.88), and E (0.25) since they represent positive or very weak correlations.

Step 3: Assessing Correlation Strength

The scatterplot points cluster fairly close to a line. This indicates a strong negative correlation, closer to -1 than to 0.

Final Answer: The most reasonable estimate is C (-0.95).

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