Scatter Plot and Line of Best Fit Worksheets With Answer Keys

These six scatter plot worksheets take students from plotting points to judging a line of best fit, with an answer key under each one. Every data set is small enough to plot by hand on graph paper, and every one opens in the free scatter plot maker so you can change the numbers, print a clean version or project the answer. They were written for students meeting scatter plots, correlation and lines of best fit for the first time, and each worksheet targets one idea.

How to Use These Worksheets

What Each Worksheet Covers

Printing and Changing the Data

Print this page and hand out the tables and questions; the answer keys follow each worksheet, so keep them back or cut them off. To make a new version, press the “Open” button under a worksheet: the data opens in the scatter plot maker, where you can edit any number, switch the line of best fit on or off, and download a PNG or SVG of the plot for your own handout.

Ground Rules for Students

• Put the first column on the horizontal (x) axis and the second on the vertical (y) axis.
• Label both axes with units.
• When you draw a line by eye, aim for about as many points above the line as below.
• Say “goes with”, not “causes”.

All data sets are made up for practice, with realistic numbers. The answer keys were calculated with least squares, the same method used by Excel, Google Sheets and graphing calculators, and rounded to the precision shown.

Worksheet 1: Arm Span and Height

Ten students measured their arm span (fingertip to fingertip) and their height, in inches.

Questions

1. Make a scatter plot with arm span on the x-axis and height on the y-axis.
2. Describe the direction of the relationship: positive, negative or none?
3. Is the relationship strong or weak? Explain using the plot.
4. Draw a line of best fit by eye. Pick two points on your line and find its equation.
5. Use your line to predict the height of a student with a 65 inch arm span.

Answer Key

1. See the plot above.
2. Positive: longer arm spans go with greater heights.
3. Strong: the points lie very close to a straight line. The correlation r is about 0.99.
4. Hand-drawn lines will vary. The least squares line is y = 0.974x + 2.21. A slope close to 1 means height rises about one inch for each extra inch of arm span.
5. About 65.5 inches. This is exactly the mean height, because 65 is the mean arm span and the least squares line always passes through the point of the two means.

Open Worksheet 1 in the scatter plot maker

Worksheet 2: Temperature and Hot Cocoa

A school snack stand recorded the day’s high temperature and the number of cups of hot cocoa sold on nine days.

Questions

1. Make a scatter plot with temperature on the x-axis.
2. What kind of correlation do you see?
3. The line of best fit is y = −1.087x + 85.8. Explain the slope in a sentence, with units.
4. Predict the cups sold on a 42°F day.
5. The intercept is 85.8. Does it make sense to use it to predict sales on a 0°F day? Why or why not?

Answer Key

1. See the plot above.
2. A strong negative correlation: warmer days go with fewer cups sold. r is about −0.998.
3. For each extra degree Fahrenheit, the stand sells about 1.09 fewer cups of cocoa, on average.
4. −1.087 × 42 + 85.8 ≈ 40 cups.
5. No. The data only covers 20°F to 60°F. A prediction at 0°F is outside that range, so the line may not hold there. Predictions should stay inside the range of the data.

Open Worksheet 2 in the scatter plot maker

Worksheet 3: Shoe Size and Math Score

Twelve students gave their shoe size and their score on a math test.

Questions

1. Make a scatter plot with shoe size on the x-axis.
2. Describe the correlation.
3. A computer gives R² = 0.003 for this data. What does that tell you?
4. Would it make sense to use shoe size to predict a math score? Explain.
5. Suppose a different class of students aged 6 to 16 showed a positive pattern between shoe size and score. Give a reason other than “big feet make you better at math”.

Answer Key

1. See the plot above.
2. No correlation. For any shoe size, the scores are spread all over the range.
3. Almost none of the differences in scores (about 0.3 percent) follow a straight line through shoe size.
4. No. Knowing the shoe size tells you nothing useful about the score.
5. Age. Older students have bigger feet and have also studied more math. A third factor can make two variables move together without one causing the other.

Open Worksheet 3 in the scatter plot maker

Worksheet 4: Growth of a Bean Plant

A student measured a bean plant once a week for eight weeks.

Questions

1. Make a scatter plot with the week on the x-axis.
2. Find the line of best fit (by eye or with a calculator) and write its equation.
3. About how much does the plant grow each week?
4. Predict the height in week 9.
5. Predict the height in week 30. Do you trust this prediction? Explain.

Answer Key

1. See the plot above.
2. y = 1.986x + 0.064, or about y = 2x.
3. About 2 cm per week, the slope.
4. 1.986 × 9 + 0.064 ≈ 17.9 cm. Week 9 is just past the data, so this is a reasonable estimate.
5. The equation gives about 59.6 cm, but week 30 is far outside the 8 weeks measured. Nothing in the data shows the plant keeps growing at the same rate for that long, so the prediction is a guess, not a result.

Open Worksheet 4 in the scatter plot maker

Worksheet 5: Prices of Used Bikes

A website lists nine used bikes of the same brand. One of them, Bike I, is a rare limited edition.

Questions

1. Make a scatter plot with age on the x-axis. Which point does not fit the pattern?
2. With all nine bikes, the line of best fit is y = −48.79x + 513.6 and R² = 0.621. Without Bike I, it is y = −40.48x + 447.1 and R² = 0.997. What did one bike do to the line?
3. Use each line to predict the price of a 5.5 year old bike. Which prediction is more believable?
4. Should Bike I be removed from the data? Give one reason to remove it and one reason to keep it.

Answer Key

1. Bike I (3 years, $600) sits far above the others.
2. It pulled the line upward and made it steeper, and it cut R² from 0.997 to 0.621, so the line describes the other bikes much worse.
3. With Bike I: about $245. Without it: about $225. The second is more believable for an ordinary bike, because it fits the eight regular listings.
4. Remove it: it is a rare edition, a different kind of bike from the others. Keep it: it is real data and not a mistake. The fair answer is to investigate the reason first, then report which line you used and why.

Open Worksheet 5 in the scatter plot maker

Worksheet 6: Residuals by Hand

A small online shop tracked its monthly ad spending and sales for six months. The line of best fit is y = 3.571x + 8.667.

Questions

1. Use the equation to find the predicted sales for each month.
2. Find each residual: actual y minus predicted y.
3. Which month had the largest positive residual? What does a positive residual mean?
4. Add up the six residuals. What do you notice?
5. Explain the slope in a sentence, with units.

Answer Key

1. and 2. See the table.
2. Month 3, with a residual of about 1.62. A positive residual means the point is above the line: actual sales beat the prediction.
3. They add up to 0, apart from rounding. For a least squares line, the positive and negative residuals always balance.
4. Each extra $100 of ad spending goes with about $3,571 more in sales, on average. That does not prove the ads caused the sales.

Open Worksheet 6 in the scatter plot maker

Tips for Teaching Scatter Plots

Start by Eye, Then Compare

OpenStax’s Introductory Statistics (2023 edition) suggests a class exercise where every student fits a line by eye and finds its equation from two points, then the class compares. Everyone gets a slightly different line, which is the best way to show why statisticians agree on one rule, least squares, that picks a single best line.

Always Ask for the Slope in Words

The textbook’s advice is to interpret the slope in plain English, in the context of the data. “The slope is 2” earns half marks. “The plant grows about 2 cm per week” earns full marks.

Make Prediction Limits a Habit

Every worksheet above with a prediction includes one inside the data and one outside it. OpenStax warns that the line is only reliable within the range of the x values you measured.

Separate Correlation From Cause

The NIST/SEMATECH e-Handbook of Statistical Methods says a scatter plot reveals association, and that no statistical procedure can prove cause and effect. Worksheets 3 and 6 build that habit into the answers.

For the full explanations behind these questions, read what a scatter plot is and the line of best fit guide. Students working in a spreadsheet can follow how to make a scatter plot in Excel and Google Sheets.