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.
Use a calculator to find the line of best fit, then answer each question.
Find the equation of the line of best fit (least squares).xy225425648−1410−1912−15y=−5x+36
Use the line of best fit to predict y when x=15.xy3−145−367−379−4111−5813−84−87
Find the residual at x=4, using the line of best fit.xy2204−106−228−2610−3212−50−8
y=3.5x+68 predicts test score (y) from hours studied (x). Interpret the y-intercept.When a student studies 0 hours, the predicted test score is about 68 points.
The residual plot for a linear model is shown. Is a line a good model for the data?Yes: the residuals are scattered with no pattern
Find the equation of the line of best fit (least squares).xy346446549655764876y=6x+23
Use the line of best fit to predict y when x=17.xy344574786990119613114138
Find the residual at x=13, using the line of best fit.xy31553774795911731375−6
y=−5.5x+100 predicts number of shirts sold (y) from price in dollars (x). Interpret the y-intercept.When the price is 0 dollars, the predicted number of shirts sold is about 100 shirts.
The residual plot for a linear model is shown. Is a line a good model for the data?Yes: the residuals are scattered with no pattern
Find the equation of the line of best fit (least squares).xy237345444548657757y=4x+30
Use the line of best fit to predict y when x=16.xy234−36−128−2410−3912−57−76
Find the residual at x=10, using the line of best fit.xy406−128−2110−2312−2814−606
y=18x+96 predicts ice cream sales (y) from temperature in degrees (x). Interpret the slope.For each additional degree, the predicted ice cream sales increases by about 18 dollars.
The residual plot for a linear model is shown. Is a line a good model for the data?No: the residuals form a curve, so the data are not linear
Find the equation of the line of best fit (least squares).xy31753575096211711377y=6x+4
Use the line of best fit to predict y when x=14.xy215416−108−1410−2112−55−56
Find the residual at x=9, using the line of best fit.xy34527−99−1511−1613−26−2
y=11.5x+153 predicts ice cream sales (y) from temperature in degrees (x). Interpret the y-intercept.When the temperature is 0 degrees, the predicted ice cream sales is about 153 dollars.
The residual plot for a linear model is shown. Is a line a good model for the data?No: the residuals form a curve, so the data are not linear
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).xy17273−24−65−56−13→ y=−4x+12
Predict from the line
Use the line of best fit to predict y when x=7.xy17273−24−65−56−13→ −16
Find a residual
Find the residual at x=2, using the line of best fit.xy17273−24−65−56−13→ 3
Interpret the slope and intercept
y=−5x+247 predicts 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
The residual plot for a linear model is shown. Is a line a good model for the data?→ Yes: the residuals are scattered with no pattern
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 5: find the line of best fit, predict from the line, find a residual, interpret the slope and intercept and read a residual plot. 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.