Curve Fitting (Trend Analysis And Prediction)

For a set of data points (x, y), this algorithm can be used to fit the data to any of the following curves:

1. Straight line (linear regresion); y = A + b*x
2. Exponential curve; y = A*EXP(b*x); nb a > 0
3. Logarithmic curve; y = A + b*LN(x)
4. Power curve; y = A*x^b; nb a > 0

The coefficient of determination is R2 (how well does the curve fit)
-- Prepare test data
CREATE TABLEcf
(
x decimal(38, 10),
y decimal(38, 10)
)

-- Calculate Linear regression
INSERTcf
SELECT40.5, 104.5 UNION ALL
SELECT38.6, 102 UNION ALL
SELECT37.9, 100 UNION ALL
SELECT36.2, 97.5 UNION ALL
SELECT35.1, 95.5 UNION ALL
SELECT34.6, 94

SELECT'Linear regression' AS Type, A, b, R2
FROMdbo.fnCurveFitting(1)
UNION ALL
SELECT'Bestfit = ' + CAST(Type AS VARCHAR), A, b, R2
FROMdbo.fnBestFit()

-- Calculate Exponential regression
DELETE
FROMcf

INSERTcf
SELECT.72, 2.16 UNION ALL
SELECT1.31, 1.61 UNION ALL
SELECT1.95, 1.16 UNION ALL
SELECT2.58, .85 UNION ALL
SELECT3.14, .5

SELECT'Exponential regression' AS Type, A, b, R2
FROMdbo.fnCurveFitting(1)
UNION ALL
SELECT'Bestfit = ' + CAST(Type AS VARCHAR), A, b, R2
FROMdbo.fnBestFit()

-- Calculate Logarithmic regression
DELETE
FROMcf

INSERTcf
SELECT3, 1.5 UNION ALL
SELECT4, 9.3 UNION ALL
SELECT6, 23.4 UNION ALL
SELECT10, 45.8 UNION ALL
SELECT12, 60.1

SELECT'Logarithmic regression' AS Type, A, b, R2
FROMdbo.fnCurveFitting(1)
UNION ALL
SELECT'Bestfit = ' + CAST(Type AS VARCHAR), A, b, R2
FROMdbo.fnBestFit()

-- Calculate Power regression
DELETE
FROMcf

INSERTcf
SELECT10, .95 UNION ALL
SELECT12, 1.05 UNION ALL
SELECT15, 1.25 UNION ALL
SELECT17, 1.41 UNION ALL
SELECT20, 1.73 UNION ALL
SELECT22, 2 UNION ALL
SELECT25, 2.53 UNION ALL
SELECT27, 2.98 UNION ALL
SELECT30, 3.85 UNION ALL
SELECT32, 4.59 UNION ALL
SELECT35, 6.02

SELECT'Power regression' AS Type, A, b, R2
FROMdbo.fnCurveFitting(1)
UNION ALL
SELECT'Bestfit = ' + CAST(Type AS VARCHAR), A, b, R2
FROMdbo.fnBestFit()

DROP TABLE cf
Peter Larsson
Helsingborg, Sweden