Line of Best Fit and R²: Choosing the Right Trend Line

By Dr. Ahmed Mortuza Saleque · Updated November 11, 2026 · How we check our content

The short answer

A line of best fit is the line that makes the squared vertical distances from the points as small as possible. R squared (R²) is the share of the variation in y that the line explains, from 0 to 1. In the example below, y = 4.48x + 46.9 has R² = 0.99. Pick the fit type that matches the shape of the data, not the highest R² alone.

Open the Data Plotter →

Scatter plot of study hours against test score with a linear line of best fit, equation y = 4.48x + 46.9 and R squared of 0.99 — Tap the image to enlarge it. Free to share with a link to this page.

Worked example: the data

Eight students: hours of study and test score.

Hours studied (x)	Test score (y)
1	52
2	55
3	61
4	64
5	70
6	72
7	79
8	83

Calculating the line of best fit

Means: x̄ = 4.5 and ȳ = 67.0.
Slope = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)² = 188 ÷ 42 = 4.48 points per hour.
Intercept = ȳ − slope × x̄ = 67.0 − 4.48 × 4.5 = 46.9.
Line of best fit: score = 4.48 × hours + 46.9.
R² = 0.992: the line explains 99.2% of the variation in scores.

Paste the two columns into the Data Plotter and choose Linear regression to get the same equation and R² drawn on the chart.

What R² does and does not tell you

R² does not prove cause. Ice cream sales and drownings correlate because both rise in summer.
A high R² can hide the wrong shape. Always look at the residual plot: a curve in the residuals means the model is wrong.
Adding polynomial terms always raises R², even when the extra wiggles are noise.
For a straight line, R² is the square of the correlation coefficient r. The correlation coefficient calculator gives r directly.

The Data Plotter labels fits with these bands.

R²	Label	Meaning
Above 0.9	Excellent	The fit follows the data closely
0.7 to 0.9	Good	Clear trend with some scatter
0.5 to 0.7	Moderate	A trend, but much is unexplained
Below 0.5	Weak	The model explains little

Choosing the fit type

Fit	Equation	Use when	Requirement
Linear	y = a + bx	Constant rate of change	None
Exponential	y = a·e^(bx)	Growth or decay by a constant percentage	y > 0
Logarithmic	y = a + b·ln(x)	Fast rise that levels off	x > 0
Power	y = a·x^b	Scaling laws, such as area and length	x and y > 0
Polynomial	y = a + bx + cx² …	One or two bends, within the data range	Use the lowest degree that works

Example: when linear is the wrong choice

A bacterial culture is counted every hour: 100, 135, 180, 245, 330, 445 and 600. A straight line gives R² = 0.94, which sounds good, but its residuals curve. An exponential fit, y = 99.8·e^(0.299x), gives R² above 0.999 and matches the biology: the count grows about 35% an hour and doubles every ln 2 ÷ 0.299 = 2.3 hours.

The Data Plotter's Model Comparison chart fits linear, polynomial, exponential, logarithmic and power models at once and ranks them by R², so you can see this in one click.

Common questions

How do you find the line of best fit?

Use least squares: slope = Σ(x − x̄)(y − ȳ) ÷ Σ(x − x̄)², intercept = ȳ − slope × x̄. A plotting tool does this automatically.

What is a good R squared value?

It depends on the field. Physical experiments often exceed 0.95; social and biological data with R² of 0.3 to 0.6 can still be useful.

Can R squared be negative?

For a least-squares fit with an intercept, no. It can be negative when a model is forced through a point or judged on new data, meaning it predicts worse than the mean.

Should I extrapolate the line beyond my data?

Carefully. The fit is only checked within the data range; predictions far outside it, such as 20 hours of study, can be unrealistic.