Fit Exponential Curve: Step-by-Step Calculation Guide
Learn how to fit an exponential curve using regression and correlation analysis. This detailed guide provides a step-by-step calculation process with examples, from transforming the equation to finding the final fitted equation. Understand the procedure to fit an exponential curve efficiently.
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Presentation Transcript
STA404 Regression & Correlation Analysis How to fit an Exponential Curve? Procedure and step by step calculation with example II
How to fit an Exponential Curve Example: Fit an exponential curve to data given below: Y = b aX X Y 1 2 3 4 5 6 2.98 4.26 5.21 6.10 6.80 7.50 2
Transformation of given equation Non-linear form Linear form = b Y aX How . ? Taking log on both sides 3
Now it is linear form = + Y A bX 1st normal equation: (Apply on both sides) 2nd normal equation: (Multiply with X and then Apply on both sides) 4
Required Calculation (Log X)*(Log Y) X Y Log Y Log X (Log X)^2 1 2.98 2.98 0.0000 0.0000 0.0000 2 4.26 4.26 0.3010 0.0906 0.1895 3 5.21 5.21 0.4771 0.2276 0.3420 4 6.10 6.10 0.6021 0.3625 0.4728 5 6.80 6.80 0.6990 0.4886 0.5819 6 7.50 7.50 0.7782 0.6055 0.6809 Total - 4.3133 2.8574 1.7749 2.2672 5
Solving Normal Eqsfind b = nA b X + Y ( ) 2 A X = + X Y b X 6
Putting b get value of A Now we put the value of b = 0.515 in Eq1 and solve as = nA b X + Y 7
Converting back = log a = A a log( ) anti A 8
How to Use Windows Calculator For Anti log Write value Then Press For log Write value Then Press 9
Hence the fitted equation becomes = b Y aX = Y 10
Recap Make suitable Transformation Get new equation Given Data Solve Normal Eqs and Do Table Calculations Final Equation Converted back 11
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