Concept explainers
Perform the same computation as in Sec. 20.1, but use linear regression and transformations to fit the data with a power equation. Assess the result.
To calculate: A power equation fit to the data for specific growth rate and available food the data using linear regression equation and transformation.
Answer to Problem 1P
Solution: The power equation to fit the data for specific growth rate and available food is
Explanation of Solution
Given Information: Data for specific growth rate
Formula used: A linear regression equation is given as
Here,
Power equation can be obtained from the linear regression equation as,
Here,
Calculation: For the given data,
Consider logarithmic terms and evaluate the summationsas,
Calculate the value of
Here,
Thus,
Simplify,
Substitute the values from the summation table and solve as,
Calculate the value of
Here,
Thus,
Simplify,
Substitute the values from the summation table and solve as,
Thus, the linear regression equation is,
Therefore,
Thus, the power equation fit to the datais written as,
The plot for both the linear and the power models is obtained as,
Hence, the power equation fit gives better approximation than the linear regression fit.
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Chapter 20 Solutions
Numerical Methods for Engineers
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