Mathematics · University
Least-squares slope from centered sums
Sxx must be positive. These are centered sums, so no extra division by sample size is required.
Method and conditions
Sxx must be positive. These are centered sums, so no extra division by sample size is required.
b₁ = Sxy/Sxx
Worked examples
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
A simple least-squares fit with an intercept has centered sums Sxx = 172 and Sxy = 140. Find the fitted slope. Round the final result to 4 decimal places if needed.
Solve the centered normal equation: 172b₁ = 140.
0.814
Try it
A simple least-squares fit with an intercept has centered sums Sxx = 85 and Sxy = 104. Find the fitted slope. Round the final result to 4 decimal places if needed.
A simple least-squares fit with an intercept has centered sums Sxx = 6 and Sxy = -49. Find the fitted slope. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 1.2235
Solve the centered normal equation: 85b₁ = 104.
- -8.1667
Solve the centered normal equation: 6b₁ = -49.
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