Regression Analysis
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.
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. DUse 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
DUse 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