SAT question 3d985614 (Two-variable Data Models And Scatterplots)

Question

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?

14

Difficulty:Medium

A

$y = 0.82 x + 3.30$

B

$y = 0.82 x - 0.82$

C

$y = 3.30 x + 0.82$

D

$y = 3.30 x - 3.30$

College Board · Accepted Answer

The correct answer is C. 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 (0, 1) . An equation for the line can be written in slope-intercept form, y = m x + b , where m is the slope and b is the y -coordinate of the y -intercept. The equation y = 3.30x + 0.82 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.

CookSAT · Answer

Note: The regression gives m=3.25 and b=0.75, so choose the answer choice with the closest coefficients.

Explanation

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Why the other choices are wrong

SAT Question 3d985614: Two-variable Data Models And Scatterplots answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong