Question 1.5.3: Fitting a Power Function with a Known Exponent Fit the power...
Fitting a Power Function with a Known Exponent
Fit the power function y = b x^{m} to the data y_{i} . The value of m is known.
The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.
Learn more on how we answer questions.
The least-squares criterion is
J = \sum^{n}_{i=1}{(bx^{m} − y_{i})^{2}}
To obtain the value of b that minimizes J , we must solve ∂J/∂b = 0.
\frac{∂J}{∂b} = 2 \sum^{n}_{i=1} {x^{m}_{i} (b x^{m}_{i} − y_{i}) = 0}
This gives
b = \frac{\sum^{n}_{i=1} {x^{m}_{i} y_{i}}}{\sum^{n}_{i=1} {x^{2m}_{i}}} (1)
Related Answered Questions
Question: 1.5.2
Verified Answer:
Subtracting 10 from all the x values and 11 from a...
Question: 1.5.1
Verified Answer:
These data do not lie close to a straight line whe...
Question: 1.4.2
Verified Answer:
First obtain the flow rate data in ml/s by dividin...
Question: 1.4.1
Verified Answer:
Common sense tells us that the water temperature w...
Question: 1.3.2
Verified Answer:
The essence of the linearization technique is to r...
Question: 1.3.1
Verified Answer:
The plot is shown in Figure 1.3.2. Common sense te...
Question: 1.3.3
Verified Answer:
The truncated Taylor series for this function is
[...
Question: 1.6.6
Verified Answer:
First obtain the flow rate data in ml/s by dividin...
Question: 1.6.5
Verified Answer:
First obtain the flow rate data in ml/s by dividin...
Question: 1.6.4
Verified Answer:
From Example 1.4.1, we learned that the relative t...