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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Medium

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. Which of the following is closest to the difference between the y-coordinate of the data point with x equals 1 and the y-value predicted by the line of best fit at x equals 1 ?

The figure presents a scatterplot in the x y plane. The numbers 0 through 6, in increments of 1, are indicated on the x-axis. The numbers 6 through 12, in increments of 1, are indicated on the y-axis. There are 10 data points in the scatterplot. The data points begin at the point with coordinates 0 comma 12, and trend downward and to the right. The coordinates of the data points are as follows. Note that all values are approximate. Point 1. 0, comma 12. Point 2. 0 point 8, comma 11. Point 3. 1, comma 12. Point 4. 1 point 5, comma 10 point 3. Point 5. 2, comma 10. Point 6. 2 point 2, comma 9 point 2. Point 7. 3, comma 9. Point 8. 3 point 5, comma 8. Point 9. 3 point 8, comma 8 point 3. Point 10. 4, comma 7. A line of best fit is also drawn. The line slants downward and to the right, passing through the point with approximate coordinates 1 comma 11, and the point with approximate coordinates 4 comma 7 point 5.

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Explanation

Choice A is correct. The data point with x equals 1 has a y-coordinate of 12. The y-value predicted by the line of best fit at x equals 1 is approximately 11. The difference between the y-coordinate of the data point and the y-value predicted by the line of best fit at x equals 1 is 12 minus 11, or 1.

Choices B and C are incorrect and may result from incorrectly reading the scatterplot. Choice D is incorrect. This is the y-coordinate of the data point at x equals 1.