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11.03 Lines of best fit

Adaptive
Worksheet

Interactive practice questions

The following scatter plot shows the data for two variables, $x$x and $y$y.

A scatter plot with an x-axis labeled from 0 to 10 and a y-axis labeled from 0 to 10. Both axes are in increments of 1. Gray gridlines divide the plane into square units. Nine points are plotted on the grid:$\left(1,2\right)$(1,2), $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(4,5\right)$(4,5), $\left(5,6\right)$(5,6), $\left(6,5\right)$(6,5), $\left(7,7\right)$(7,7), and $\left(8,7\right)$(8,7). The coordinates are not explicitly labeled.
a

Determine which of the following graphs contains the line of best fit.

A scatter plot with an x-axis labeled from 0 to 10 and a y-axis labeled from 0 to 10. Both axes are in increments of 1. Gray gridlines divide the plane into square units. Nine points are plotted on the grid: $\left(1,2\right)$(1,2), $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(4,5\right)$(4,5), $\left(5,6\right)$(5,6), $\left(6,5\right)$(6,5), $\left(7,7\right)$(7,7), and $\left(8,7\right)$(8,7). A green line passes through the graph at an upward diagonal slope that follows the trend of the points, starting near the origin and extending near the top-right corner. The points are near the green line (some are above and some are below the line). The coordinates are not explicitly labeled.
A
A scatter plot with an x-axis labeled from 0 to 10 and a y-axis labeled from 0 to 10. Both axes are in increments of 1. Gray gridlines divide the plane into square units. Nine points are plotted on the grid: $\left(1,2\right)$(1,2), $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(4,5\right)$(4,5), $\left(5,6\right)$(5,6), $\left(6,5\right)$(6,5), $\left(7,7\right)$(7,7), and $\left(8,7\right)$(8,7). A green line passes through the graph at an upward diagonal slope, starting near the origin and extending near the top-right corner. Most of the points are below the green line. All coordinates are not explicitly labeled.
B
A scatter plot with an x-axis labeled from 0 to 10 and a y-axis labeled from 0 to 10. Both axes are in increments of 1. Gray gridlines divide the plane into square units. Nine points are plotted on the grid: $\left(1,2\right)$(1,2), $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(4,5\right)$(4,5), $\left(5,6\right)$(5,6), $\left(6,5\right)$(6,5), $\left(7,7\right)$(7,7), and $\left(8,7\right)$(8,7). A green line passes through the graph at an upward diagonal slope, starting near the origin and extending near the top-right corner. Most of the points are above the green line. All coordinates are not explicitly labeled.
C
A scatter plot with an x-axis labeled from 0 to 10 and a y-axis labeled from 0 to 10. Both axes are in increments of 1. Gray gridlines divide the plane into square units. Nine points are plotted on the grid: $\left(1,2\right)$(1,2), $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(4,5\right)$(4,5), $\left(5,6\right)$(5,6), $\left(6,5\right)$(6,5), $\left(7,7\right)$(7,7), and $\left(8,7\right)$(8,7). A green line passes through the graph at an upward diagonal slope but does not follow the trend of the points, starting near the origin and extending near the top-right corner. Points are plotted above and below the green line. All coordinates are not explicitly labeled.
D
b

Use the line of best fit to estimate the value of $y$y when $x=4.5$x=4.5.

A scatter plot with an x-axis labeled from 0 to 10 and a y-axis labeled from 0 to 10. Both axes are in increments of 1. Gray gridlines divide the plane into square units. Nine points are plotted on the grid: $\left(1,2\right)$(1,2), $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(4,5\right)$(4,5), $\left(5,6\right)$(5,6), $\left(6,5\right)$(6,5), $\left(7,7\right)$(7,7), and $\left(8,7\right)$(8,7). The best fit line, which is green in color, passes through the graph at an upward diagonal slope, starting near the origin and extending near the top-right corner. The points are near the best fit line but their coordinates are not explicitly labeled.

$4.5$4.5

A

$5$5

B

$5.5$5.5

C

$6$6

D
c

Use the line of best fit to estimate the value of $y$y when $x=9$x=9.

$6.5$6.5

A

$7$7

B

$8.4$8.4

C

$9.5$9.5

D
Medium
1min

The following scatter plot graphs data for the number of people in a room and the room temperature collected by a researcher.

Medium
1min

The following scatter plot graphs data for the number of copies of a particular book sold at various prices.

Medium
1min

The following scatter plot graphs data for the number of copies of a particular book sold at various prices.

Medium
1min
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Outcomes

8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

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