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AP®StatisticsCollege BoardExam QuestionsUnit 2: Exploring Two-Variable DataScatterplots & Regression

Scatterplots & Regression (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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For which of the following scatterplots is the correlation between x and y closest to negative 1?

  • Scatterplot to determine the relationship between 'x' (0 to 100) and 'y' (0 to 40). Points decrease from top left to bottom right, closely following a trend.
  • Scatterplot to determine the relationship between 'x' (0 to 100) and 'y' (0 to 40). Points decrease from top left to bottom right, loosely following a trend.
  • Scatterplot to determine the relationship between 'x' (0 to 100) and 'y' (0 to 40). Points show no clear straight-line trend.
  • Scatterplot to determine the relationship between 'x' (0 to 100) and 'y' (0 to 40). Points increase from top left to bottom right, loosely following a trend.
  • Scatterplot to determine the relationship between 'x' (0 to 100) and 'y' (0 to 40). Points increase from top left to bottom right, closely following a trend.

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2
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A large bakery decided to conduct some consumer research to determine how much customers liked their products. They asked a selection of new customers (those who had not tried any food from the bakery before) and regular customers (those who regularly bought items from the bakery) to rate 20 different bakery products. Ratings were given on a scale from one to ten, where one was "terrible" and ten was "exceptional." For each bakery product, the average rating by new customers and the average rating by regular customers was calculated, and the scatterplot below was constructed. The horizontal axis represents the rating from new customers, and the vertical axis represents the rating given by regular customers. An individual data point, therefore, represents the rating of a single bakery product.

Scatter plot comparing New Customer Ratings on the x-axis with Regular Customer Ratings on the y-axis. Twenty points are plotted and follow a trend that starts at the top left and comes down toward the middle right on the graph.

Which of the following statements is justified by the scatter plot?

  • The bakery products that regular customers liked the best also tended to be the bakery products that new customers liked the best, but regular customers tended to give a higher rating.

  • The bakery products that regular customers liked the best also tended to be the bakery products that new customers liked the best, but regular customers tended to give a lower rating.

  • The bakery products that regular customers liked the best tended to be the bakery products that new customers liked the least, but regular customers tended to give a higher rating.

  • The bakery products that regular customers liked the best tended to be the bakery products that new customers liked the least, but regular customers tended to give a lower rating.

  • The bakery products that regular customers liked the best tended to be the bakery products that new customers liked the least, but each group tended to give the same rating.

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3
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A study into the effects of smoking looked at the number of years that a person from the United States had smoked and their lung capacity. It was found that people who had smoked an average of five cigarettes per day for six years were nine times as likely to have a lower lung capacity than someone who had no history of smoking. Which of the following statements could be made about this study?

  • Smoking decreases lung capacity.

  • There is an association between smoking and lung capacity, but not necessarily a causal relationship.

  • There is a correlation between smoking and lung capacity, but not necessarily an association.

  • The association between smoking and lung capacity is positive.

  • Smoking causes a reduction in lung capacity for people in the United States, but not necessarily in other countries.

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4
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A scatter plot of exposure to sunlight, in minutes, versus corresponding vitamin D level, in ng/mL, is shown below. One of the points in the graph is labeled A.

Scatterplot showing the relationship between exposure to sunlight (minutes) and vitamin D level (ng/mL), with a generally increasing trend. A point labeled A is located in the top right of the graph above the general trend of the rest of the points.

If the point labeled A is removed, which of the following statements would be true?

  • The slope of the least squares regression line is unchanged, and the correlation coefficient increases.

  • The slope of the least squares regression line is unchanged, and the correlation coefficient decreases.

  • The slope of the least squares regression line decreases, and the correlation coefficient increases.

  • The slope of the least squares regression line decreases, and the correlation coefficient decreases.

  • The slope of the least squares regression line increases, and the correlation coefficient increases.

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5
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A student's number of hours studied and their corresponding percentage score in a science quiz were recorded. The data resulted in a least squares regression line with the equation y equals 3.21 x plus 66.58 and were used to create the residual plot shown below.

Residual plot showing the relationship between hours of study (x-axis) and residuals (y-axis), with residuals ranging from -5 to 5 and study hours from zero to eight.

Which of the following values is closest to the actual quiz score for the student who had studied for six hours?

  • 90

  • 88

  • 86

  • 83

  • 80

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