Scatter Graphs · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Lines of Best Fit on Scatter Graphs

Mathematics · Data & Statistics · ages 13-14
Name ______________________   Date ____________

  1. If a scatter graph shows no correlation, the points still always line up neatly on a straight line.

    Circle one:   True   False

  2. Maya measures the height of a plant every week for 10 weeks. She wants to plot week number against plant height on a scatter graph. What should she put on the x-axis?

    • The week number, because it is the variable she chooses in advance
    • The plant height, because it is the most interesting number
    • Either one, because it never matters
    • The plant height, because it always goes on the x-axis

  3. A line of best fit must pass exactly through as many of the data points as possible.

    Circle one:   True   False

  4. Which of these is essential when setting up the axes of a scatter graph?

    • Starting every axis at zero, no matter what
    • Labels and an even, consistent scale on both axes
    • Using a different scale for every single point

  5. A line of best fit passes through (10, 30) and (20, 60) on a graph of temperature against visitors at a pool. About how many visitors would you predict at 16 degrees?

    • About 48
    • About 30
    • About 76
    • About 60

  6. A shop plots ice cream sales against millimetres of rainfall. As rainfall goes up, sales go down, and the points are spread quite widely around any straight line. What is the best description?

    • Weak negative correlation
    • Strong positive correlation
    • No correlation at all
    • Perfect negative correlation

  7. Aisha draws a line of best fit, but 8 of her 10 points end up above the line and only 2 below. What should she do?

    • Adjust the line so it better balances points above and below
    • Leave the line as it is because it touches more points that way
    • Delete the 8 points above the line so they match

  8. Your line of best fit passes through the points (2, 9) and (8, 33). Use the line to estimate the y-value when x is 5.

    Answer: ______________

  9. A line of best fit on a graph of temperature against ice cream sales passes through (0, 4) and (10, 34). Estimate the sales when the temperature is 7 degrees.

    Answer: ______________

  10. Priya draws her line of best fit by joining her first point straight to her last point, ignoring the points in between. What is wrong with this?

    • This is the correct way to draw a line of best fit
    • The line should reflect the trend of all the points, not just connect the first and last one
    • The line should be curved instead of straight
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Lines of Best Fit on Scatter Graphs W1-mt_BdAeZJUOir-s1

  1. False · False. No correlation means there is no straight line trend at all. The points look like a random scattered cloud with no clear direction.
  2. The week number, because it is the variable she chooses in advance · The variable you control or choose first, here the week number, goes on the x-axis. The variable you measure or watch, the height, goes on the y-axis.
  3. False · False. Real data is messy, so the line of best fit almost never hits the points exactly. It just balances them, with about as many above as below.
  4. Labels and an even, consistent scale on both axes · Without labels and an even scale, no one can tell what the points mean or read them accurately.
  5. About 48 · The slope is 3 visitors per degree and the line crosses the axis at 0, so at 16 degrees the prediction is 48 visitors.
  6. Weak negative correlation · The two variables move in opposite directions, so the correlation is negative. The wide spread of points means it is weak rather than strong.
  7. Adjust the line so it better balances points above and below · A good line of best fit splits the points roughly evenly, not just touches as many as possible.
  8. 21 · The line rises 24 over a run of 6, so its slope is 4. Its equation is y = 4x + 1, and at x = 5 the estimate is 21.
  9. 25 · The slope is 3 sales per degree and the line starts at 4, so the equation is y = 3x + 4. At 7 degrees the estimate is 25 sales.
  10. The line should reflect the trend of all the points, not just connect the first and last one · Two points can be misleading if they're unusual. The line needs to balance every point, not just the end ones.
Worksheet · LightMySky