Mathematics · University
Least-squares slope from centered sums · formula reference
Sxx must be positive. These are centered sums, so no extra division by sample size is required.
Formula
Sxx must be positive. These are centered sums, so no extra division by sample size is required.
b₁ = Sxy/Sxx
Worked example
A simple least-squares fit with an intercept has centered sums Sxx = 125 and Sxy = 93. Find the fitted slope. Round the final result to 4 decimal places if needed.
Solve the centered normal equation: 125b₁ = 93.
0.744
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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