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.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
When a scatter plot shows a roughly linear trend, a straight line can summarize the whole cloud of points in one simple model. Eighth graders fit this line informally, by eye, often with a piece of spaghetti or a clear ruler. A good line follows the direction of the data, passes through the middle of the cloud, and leaves roughly as many points above it as below along its whole length, not just overall.
Students then judge how good the model is. If the points hug the line closely, the line describes the relationship well and predictions made from it are reasonably trustworthy. If points are spread far from the line, or form a curve that the line cuts across, the model is weak or inappropriate. Comparing two candidate lines and arguing which fits better, using the distances from points to each line, is a natural task. No formulas for least-squares regression are needed; the goal is a sensible, defensible line and an honest description of the fit.
Many data sets do not start at zero. The line should follow the data, crossing the vertical axis wherever the trend suggests.
Joining the leftmost and rightmost points ignores everything in between, and an outlier at either end can tilt the line badly.
A line with half the points above it could still have all the high points on the left. Points should be balanced across the whole range.
If the pattern bends, a straight line will be too high in some places and too low in others. A line is the wrong model in that case.
Data on study hours (x) and quiz score (y) for six students: (1, 62), (2, 68), (3, 71), (4, 78), (5, 83), (6, 87). Line A is y = 5x + 57. Line B is y = 3x + 65. Which line fits better?
Answer: Line A, y = 5x + 57, fits better: every point is within 1 point of it.
Give each student a printed scatter plot and a piece of uncooked spaghetti to position as a line of best fit, then compare lines across the room. The variety starts a discussion about what makes a line good. Overlaying two lines on the board and measuring vertical distances to the points gives students a fair way to settle disagreements.
Assessments may show several lines drawn on the same scatter plot and ask which best fits the data, or ask whether a linear model is appropriate at all. Encourage students to mention both the direction of the trend and how closely the points cluster around the line.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: C) A line through the middle of the data with points balanced above and below
A line of best fit follows the trend through the middle of the cloud, with points balanced on both sides along its length.
Answer: B) No, the association is nonlinear
A U-shaped pattern curves, so a straight line would be far from many points. A linear model is not appropriate.
Answer: 3
The line predicts y = 2(5) + 10 = 20 at x = 5. The point is 23 - 20 = 3 units above the line.
Answer: D) Plot X's line is a better model
The closer the points are to the line, the better the line models the data.
Answer: 5
Line Q has the smaller total gap, 9 units, which is 14 - 9 = 5 units less than Line P.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
A full lesson with slides, activities and an exit ticket on fitting a line to scatter plot data, pitched to grade 8 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 8.SP.A.2 with an answer key, ready in about a minute.
Make a worksheet βTurn fitting a line to scatter plot data into a quiz students answer online that marks itself, with a class summary for you.
Build a test βNo. In grade 8 the line is fitted informally by eye and judged visually. Calculating a least-squares regression line is high school work.
It follows the direction of the data, passes through the middle of the points, and has points balanced above and below it across the whole range.