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Find the least squares regression quadratic polynomial for the data points. (Let x be the independent variable and y be the dependent variable.) (0, 0), (2, 12), (3, 36), (4, 72) 6x² - 6x

Find the least squares regression quadratic polynomial for the data points. (Let x be the independent variable and y be the dependent variable.) (0, 0), (2, 12), (3, 36), (4, 72) 6x² - 6x

Advanced Engineering Mathematics
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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**Problem Statement:** Find the least squares regression quadratic polynomial for the data points. (Let \( x \) be the independent variable and \( y \) be the dependent variable.) Data points: \((0, 0), (2, 12), (3, 36), (4, 72)\) **Proposed Solution:** The quadratic polynomial \( 6x^2 - 6x \) is suggested as the solution. **Evaluation:** The generated polynomial \( 6x^2 - 6x \) is marked with a red cross, indicating it is incorrect for modeling the given data points. **Explanation:** To find the correct least squares regression quadratic polynomial, the process involves: 1. Defining the quadratic polynomial in the form \( ax^2 + bx + c \). 2. Using the method of least squares to minimize the difference between the actual data points and the values predicted by the polynomial. 3. Solving for \( a \), \( b \), and \( c \) to best fit the data. A correct solution will result in a polynomial where the sum of the squares of the differences between the actual \( y \) values and the predicted \( y \) values is minimized.
Transcribed Image Text:**Problem Statement:** Find the least squares regression quadratic polynomial for the data points. (Let \( x \) be the independent variable and \( y \) be the dependent variable.) Data points: \((0, 0), (2, 12), (3, 36), (4, 72)\) **Proposed Solution:** The quadratic polynomial \( 6x^2 - 6x \) is suggested as the solution. **Evaluation:** The generated polynomial \( 6x^2 - 6x \) is marked with a red cross, indicating it is incorrect for modeling the given data points. **Explanation:** To find the correct least squares regression quadratic polynomial, the process involves: 1. Defining the quadratic polynomial in the form \( ax^2 + bx + c \). 2. Using the method of least squares to minimize the difference between the actual data points and the values predicted by the polynomial. 3. Solving for \( a \), \( b \), and \( c \) to best fit the data. A correct solution will result in a polynomial where the sum of the squares of the differences between the actual \( y \) values and the predicted \( y \) values is minimized.
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