The line of best fit, or least-squares regression line, is the one line that keeps the squared vertical misses as small as possible. A calculator finds it from the table; the questions are about using it, and a residual is how far a real point sits above or below the line.
Also taught in Statistics, at its own level and with its own examples.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
Answer each question. Use a calculator where a line of best fit is needed.
Find the line of best fit
Find the equation of the line of best fit (least squares).xy311.54951.56−67−7.58−179−19.510−26y=−5.5x+29
Find the equation of the line of best fit (least squares).xy4−265821081212141616141821y=1.5x−7
Find the equation of the line of best fit (least squares).xy129.5231343.5441552.5658758.5868y=5.5x+23
Find the equation of the line of best fit (least squares).xy223414678110−512−1114−2316−26y=−3.5x+29
Predict with the line of best fit
Use the line of best fit to predict y when x=10.xy1−3.52−53−12.54−155−23.56−217−32.58−33−43
Use the line of best fit to predict y when x=18.xy21347658−210−812−1414−1416−23−27
Use the line of best fit to predict y when x=12.xy212313.5419518.5621727.5824930.537
Use the line of best fit to predict y when x=20.xy49608−810−912−2314−2616−3418−41−48
Find a residual
Find the residual at x=6, using the line of best fit.xy413625830104212521456166918772
Find the residual at x=5, using the line of best fit.xy17.52632.54−45−4.56−87−13.58−161
Find the residual at x=4, using the line of best fit.xy121.5221315.549511.56471.58−2−3
Find the residual at x=7, using the line of best fit.xy36.549514.5617727.5826931.510384
Interpret the slope or intercept
y=151x+4116 predicts the number of people in a town (y) from years since 2010 (x). Interpret the y-intercept.When it is 2010 (year 0), the predicted number of people in the town is about 4116 people.
y=−7x+121 predicts the number of shirts sold (y) from price in dollars (x). Interpret the slope.For each additional dollar, the predicted number of shirts sold decreases by about 7 shirts.
y=2.5x+47 predicts test score in points (y) from hours studied (x). Interpret the slope.For each additional hour, the predicted test score increases by about 2.5 points.
y=1.5x+6 predicts a baby's weight in pounds (y) from age in months (x). Interpret the slope.For each additional month, the predicted weight increases by about 1.5 pounds.
Read a residual plot
After a line was fitted, these residuals were left. Is the line a good model?No: a curved pattern remains after the line is removed, so a line is the wrong model.
Do these residuals show that a linear model is appropriate?No: a clear curved pattern in the residuals rules out a linear model.
Would you use the least-squares line to model these data, given its residuals?Yes: an even, patternless band of residuals means the linear model is appropriate.
Is fitting a straight line reasonable for the data behind this residual plot?Yes: apart from one outlier, the residuals scatter randomly in an even band, so a line fits; the outlier should be checked.
The line of best fit is y=2x+3. The point (4,13) is in the data. Find its residual
The line predicts 2 times 4 plus 3, which is 11.
The residual is actual minus predicted.
13 minus 11.
The answer is 2.
Where students go wrong
Taking predicted minus actual. A residual is actual minus predicted, so a point above the line has a positive residual.
Also called line of best fit, linear regression, least squares regression line, trend line, regression line or residuals.
What you can put on this worksheet
Find the line of best fit
Find the equation of the line of best fit (least squares). xy1122739445262→ y=−2x+13
Predict from the line
Use the line of best fit to predict ywhen x=7. xy1122739445262→ −1
Find a residual
Find the residual at x=2, using the line of best fit. xy1122739445262→ −2
Interpret the slope and intercept
y=−5x+247 predicts the number of shirts sold (y) from price in dollars (x). Interpret the slope.→ For each additional dollar, the predicted number of shirts sold decreases by about 5 shirts.
Read a residual plot
Here are the residuals from a least-squares line. Would a linear model describe these data well? — a residual plot, labeled 0, x→ Yes: the residuals are scattered with no pattern.
A line of best fit: use it, fit it with r squared, residuals and r
The line of best fit for a data set is y=1.74x+11.72.Predict ywhen x=17, to the nearest tenth.→ y≈41.3
Questions about these worksheets
Yes. Every line of best fit sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the line of best fit questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 6: find the line of best fit, predict from the line, find a residual, interpret the slope and intercept, read a residual plot and a line of best fit: use it, fit it with r squared, residuals and r. Tick as many as you want and set how many of each, or let it spread them evenly.
Taking predicted minus actual. A residual is actual minus predicted, so a point above the line has a positive residual.