Scatter Plot & Line of Best Fit

Data Points

#	x	y

One (x, y) pair per line, or separate with semicolons. Decimals OK.

Examples

Prediction

Predict ŷ when x =

Results

Enter at least 2 data points and press Plot & Compute to see the regression line.

Line of Best Fit

ŷ = — x + —

Slope (m)

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y-intercept (b)

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Correlation (r)

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r² (determination)

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Prediction

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Linear Regression

ŷ = mx + b

Linear regression finds the line ŷ = mx + b that minimizes the sum of squared residuals — the vertical distances between each data point and the line. This is called the least-squares method.

The slope m shows the rate of change: for every 1-unit increase in x, y changes by m units. The y-intercept b is the predicted value of y when x = 0.

Formulas: m = (nΣxy − ΣxΣy) / (nΣx² − (Σx)²) and b = (Σy − mΣx) / n

Correlation Coefficient r

The Pearson correlation coefficient r measures the strength and direction of the linear relationship between x and y. It always falls between −1 and 1.

|r| ≥ 0.8 — Strong linear relationship
0.5 ≤ |r| < 0.8 — Moderate linear relationship
|r| < 0.5 — Weak or no linear relationship
Positive r → upward trend; Negative r → downward trend

r² tells you what percentage of variation in y is explained by x. For example, r = 0.9 means r² = 0.81, so 81% of the variation in y is explained by the linear relationship with x.

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