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Line of best fit - Identifying

Lesson

A line of best fit  (or "trend" line) is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. However, it always represents the general trend of the of the points, so we can determine whether there is a positive, negative or no relationship. Lines of best fit are really handy as they help us determine whether there is a relationship between two variables, which we can use to make predictions. 

To draw a line of best fit, balance the number of points above the line with the number of points below the line.

Examples

Question 1

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

A scatter plot with an $x$x-axis labeled from $0$0 to $10$10 and a $y$y-axis labeled from $0$0 to $10$10. Both axes are in increments of 1 unit. Gray gridlines divide the plane into square units. Nine points are plotted on the coordinate plane:$\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 points are plotted as solid blacks dots but the coordinates are not explicitly labeled nor stated in this problem.
  1. Determine which of the following graphs contains the line of best fit.

    A scatter plot with an $x$x-axis labeled from $0$0 to $10$10 and a $y$y-axis labeled from $0$0 to $10$10. Both axes are in increments of $1$1 unit. 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 at point approximately $(0,0.7)$(0,0.7) and extending near the top-right corner at point approximately $(10,9.2)$(10,9.2). Points $\left(1,2\right)$(1,2),$\left(4,5\right)$(4,5),$\left(5,6\right)$(5,6), and $\left(7,7\right)$(7,7) are above the green line, while points $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(6,5\right)$(6,5) and $\left(8,7\right)$(8,7) are below the green line. The points are plotted as solid blacks dots but the coordinates are not explicitly labeled nor stated in this problem.
    A
    A scatter plot with an $x$x-axis labeled from $0$0 to $10$10 and a $y$y-axis labeled from $0$0 to $10$10. Both axes are in increments of $1$1 unit. 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 at point approximately $(0,1.1)$(0,1.1) and extending near the top-right corner at point approximately $(10,9.7)$(10,9.7). Point $\left(1,2\right)$(1,2) lies on the green line, while points $\left(4,5\right)$(4,5), and $\left(5,6\right)$(5,6) are above the green line, and points $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(6,5\right)$(6,5), $\left(7,7\right)$(7,7) and $\left(8,7\right)$(8,7) are below the green line. The points are plotted as solid blacks dots but the coordinates are not explicitly labeled nor stated in this problem.
    B
    A scatter plot with an $x$x-axis labeled from $0$0 to $10$10 and a $y$y-axis labeled from $0$0 to $10$10. Both axes are in increments of $1$1 unit. 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 at point approximately $(0,0.1)$(0,0.1) and extending near the top-right corner at point approximately $(10,8.8)$(10,8.8). Point $\left(7,7\right)$(7,7) lies on the green line, while points $\left(1,2\right)$(1,2), $\left(3,3\right)$(3,3), $\left(4,5\right)$(4,5), and $\left(5,6\right)$(5,6) are above the green line, and points $\left(2,1\right)$(2,1), and $\left(6,5\right)$(6,5) are below the green line. The points are plotted as solid blacks dots but the coordinates are not explicitly labeled nor stated in this problem.
    C
    A scatter plot with an $x$x-axis labeled from $0$0 to $10$10 and a $y$y-axis labeled from $0$0 to $10$10. Both axes are in increments of $1$1 unit. 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 at point approximately $(0,1.5)$(0,1.5) and extending near the top-right corner at point approximately $(10,8.2)$(10,8.2). Points $\left(4,5\right)$(4,5),$\left(5,6\right)$(5,6), $\left(7,7\right)$(7,7) and $\left(8,7\right)$(8,7) are above the green line, while points $\left(1,2\right)$(1,2), $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3) and $\left(6,5\right)$(6,5) are below the green line. The points are plotted as solid blacks dots but the coordinates are not explicitly labeled nor stated in this problem.
    D
  2. 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 $x$x-axis labeled from $0$0 to $10$10 and a $y$y-axis labeled from $0$0 to $10$10. Both axes are in increments of $1$1 unit. 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 with an equation of $y=(78/90)*x+(54/90)$y=(78/90)*x+(54/90) passes through the graph at an upward diagonal slope that follows the trend of the points. The equation of the line is not explicitly given nor stated in the graph and problem. Points $\left(1,2\right)$(1,2),$\left(4,5\right)$(4,5),$\left(5,6\right)$(5,6), and $\left(7,7\right)$(7,7) are above the green line, while points $\left(2,1\right)$(2,1), $\left(3,3\right)$(3,3), $\left(6,5\right)$(6,5) and $\left(8,7\right)$(8,7) are below the green line. The points are plotted as solid blacks dots but the coordinates are not explicitly labeled nor stated in this problem.

    $4.5$4.5

    A

    $5$5

    B

    $5.5$5.5

    C

    $6$6

    D
  3. 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

 

 

 

 

 

 

Outcomes

MS1-12-2

analyses representations of data in order to make predictions and draw conclusions

MS1-12-7

solves problems requiring statistical processes

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