The line of best fit (trend line) is the straight line that best represents the overall trend in a scatter plot by minimizing the sum of squared vertical distances between the line and all data points. Its equation enables predictions for new x-values.
If you stretched a rubber band through a scatter plot to be as close to all points as possible, that's the line of best fit. It captures the overall trend.
Showing a random 20 of 50 problems.
Example 1
easy
The line of best fit always passes through which special point of the data?
Example 2
challenge
Two lines are proposed for data (1,2),(2,2),(3,5): line A y^โ=x and line B y^โ=1.5xโ0.5. Which has the smaller sum of squared residuals?
Example 3
medium
A line of best fit for temperature (ยฐC, x) vs ice-cream sales (units, y) is y=12xโ50. (a) Predict sales when it is 30ยฐC. (b) Below what temperature does the model predict zero or negative sales? (c) Comment on the limitation.
Example 4
medium
A scatter plot is roughly U-shaped. Is the line of best fit a good summary?
Example 5
medium
A trend line y^โ=โ3x+40 models temperature drop. Predict y^โ at x=7 and state the trend direction.
Example 6
easy
A scatter plot shows the relationship between hours studied (x) and test score (y). The data points generally trend upward. A line of best fit has equation y=5x+40. (a) Interpret the slope. (b) Predict the score for a student who studies 8 hours.
Example 7
hard
A regression line uses summary stats xห=10, yหโ=40, r=0.5, syโ=12, sxโ=4. Find the line of best fit.Regression line passing through the mean point (10, 40)
Example 8
medium
A line of best fit y^โ=2x+1 is fitted, but one extreme outlier at (10,100) pulls the line up. What problem does this illustrate?
Example 9
hard
Two students draw different lines of best fit through the same scatter plot. Student A's line: y=3x+2 (sum of squared residuals = 40). Student B's line: y=2.5x+4 (sum of squared residuals = 28). Which line is better and why?
Example 10
challenge
A line of best fit y^โ=mx+b gives y^โ=14 at x=2 and y^โ=26 at x=5. Predict y^โ at x=8.Extend the line to predict at x = 8
Example 11
medium
Trend line y^โ=0.4x+8. By how much does y^โ change when x increases by 25?How much does ลท change when x increases by 25?
Example 12
easy
In a scatter plot, the line of best fit summarizes what aspect of the data?
Example 13
challenge
A line of best fit passes through (xห,yหโ)=(4,10) and has slope b=rsxโsyโโ with r=0.8, syโ=6, sxโ=4. Find the full equation y^โ=bx+a.
Example 14
medium
Why is fitting a line of best fit inappropriate for a clearly U-shaped (curved) scatter plot?
Example 15
medium
Two points on a line of best fit are (0,9) and (3,0). What is its slope?Find the slope of the line through (0, 9) and (3, 0)
Example 16
easy
The line of best fit y^โ=4xโ7 has what y-intercept?
Example 17
easy
A trend line is y^โ=0.5x+2. Predict y^โ at x=10.Predict ลท at x = 10
Example 18
medium
Line of best fit y^โ=5x+3 is built from data with x ranging 1 to 10. Why is predicting at x=50 risky?
Example 19
hard
A line of best fit has slope 0 and intercept yหโ. What does this say about the linear relationship between x and y?
Example 20
easy
A line of best fit with slope 0 predicts y^โ to do what as x changes?