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Linear Regression Calculator — Best-Fit Line, R², Correlation & Residuals

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X values Paste a spreadsheet column or a comma/space/new-line separated list. Invalid tokens are rejected.Y values Paste a spreadsheet column or a comma/space/new-line separated list. Invalid tokens are rejected.Predict Y when X = Displayed precision

Calculated result

ŷ = 46.8 + 4.6286x

Slope b: 4.6286 · Intercept a: 46.8

Pearson r: 0.9959 · R²: 0.9918

Sxx: 17.5 · Sxy: 81 · SSE: 3.0857

Prediction at X=7: ŷ=79.2

Observed X range: 1 to 6

Regression residuals

#	X	Observed Y	Predicted Ŷ	Residual
1	1	52	51.4286	0.5714
2	2	55	56.0571	-1.0571
3	3	61	60.6857	0.3143
4	4	66	65.3143	0.6857
5	5	69	69.9429	-0.9429
6	6	75	74.5714	0.4286

Show the working

1. Compute x̄ = 3.5 and ȳ = 63.
2. Sxx = Σ(x−x̄)² = 17.5; Sxy = Σ(x−x̄)(y−ȳ) = 81.
3. Slope b = Sxy ÷ Sxx = 4.6286.
4. Intercept a = ȳ − b x̄ = 46.8.
5. For each pair, ŷ = a + bx and residual = y − ŷ.

The requested prediction lies outside the observed X range, so it is an extrapolation. The linear pattern may not continue there.

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