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Two-variable data: Models and scatterplots SAT question

Math · Problem-Solving and Data Analysis · Medium · Answer it here, explanation included.

The figure presents a scatterplot. The horizontal axis is labeled “High jump height, in feet,” and the numbers 0 through 6, in increments of 1, are indicated. The vertical axis is labeled “Long jump distance, in feet,” and the numbers 0 through 20, in increments of 2, are indicated. There are 20 dots indicated on the scatterplot. The dots begin in the lower left part of the plane, at the dot with coordinates 1 comma 2, and trend upward and to the right until they end in the upper right part of the plane, at the dot with coordinates 5 comma 15.

Each dot in the scatterplot above represents the height x, in feet, in the high jump, and the distance y, in feet, in the long jump, made by each student in a group of twenty students. The graph of which of the following equations is a line that most closely fits the data?

ExplanationShow

Choice C is correct. A line that most closely fits the data is a line with an approximately balanced number of data points above and below the line. Fitting a line to the data shown results in a line with an approximate slope of 3 and a y-intercept near the point $with coordinates 0 comma 1$ . An equation for the line can be written in slope-intercept form, $y equals, m x plus b$ , where m is the slope and b is the y-coordinate of the y-intercept. The equation $y equals, 3 point 3 0 x plus 0 point 8 2$ in choice C fits the data most closely.

Choices A and B are incorrect because the slope of the lines of these equations is 0.82, which is a value that is too small to be the slope of the line that fits the data shown. Choice D is incorrect. The graph of this equation has a y-intercept at $the point with coordinates 0 comma negative 3 point 3 0$ , not $the point with coordinates 0 comma 0 point 8 2$ . This line would lie below all of the data points, and therefore would not closely fit the data.

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Two-variable data: Models and scatterplots SAT question

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