Use quadratic regression to find a model for the following data set. (Round the terms to four decimal places.) f(x) = f(x) 1 1.9 3 5 8.6 28.1 6 8 35.1 59.6
Use quadratic regression to find a model for the following data set. (Round the terms to four decimal places.) f(x) = f(x) 1 1.9 3 5 8.6 28.1 6 8 35.1 59.6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Use quadratic regression to find a model for the following data set. (Round the terms to four decimal places.)
![**Topic: Quadratic Regression**
In this exercise, we aim to find a quadratic model for the given data set using regression. The task involves rounding the model's terms to four decimal places.
**Data Set Table:**
The table below presents the paired values of \( x \) and \( f(x) \):
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 1 & 3 & 5 & 6 & 8 \\
\hline
f(x) & 1.9 & 8.6 & 28.1 & 35.1 & 59.6 \\
\hline
\end{array}
\]
**Objective:**
Use quadratic regression to find \( f(x) \).
The notation \( f(x) = \) indicates the placeholder for the quadratic equation to be determined. The quadratic model will be in the standard form:
\[ f(x) = ax^2 + bx + c \]
The coefficients \( a \), \( b \), and \( c \) will be calculated to best fit the data points, providing an accurate representation of the underlying trend.
Please proceed with the calculations to determine \( a \), \( b \), and \( c \), rounding each to four decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c1b73f5-75c4-44c4-b4a1-5a3250c69300%2F0ff7e864-0116-4539-b742-594ef12e6c66%2F7qdzxpo_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Quadratic Regression**
In this exercise, we aim to find a quadratic model for the given data set using regression. The task involves rounding the model's terms to four decimal places.
**Data Set Table:**
The table below presents the paired values of \( x \) and \( f(x) \):
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
x & 1 & 3 & 5 & 6 & 8 \\
\hline
f(x) & 1.9 & 8.6 & 28.1 & 35.1 & 59.6 \\
\hline
\end{array}
\]
**Objective:**
Use quadratic regression to find \( f(x) \).
The notation \( f(x) = \) indicates the placeholder for the quadratic equation to be determined. The quadratic model will be in the standard form:
\[ f(x) = ax^2 + bx + c \]
The coefficients \( a \), \( b \), and \( c \) will be calculated to best fit the data points, providing an accurate representation of the underlying trend.
Please proceed with the calculations to determine \( a \), \( b \), and \( c \), rounding each to four decimal places.
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