17.6 Use least-squares regression to fit a straight line to 2 3 4 7 8 1 1.5 2 3 4 8 10 13 (a) Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot the data and the straight line. Assess the fit. (b) Recompute (a), but use polynomial regression to fit a parabola to the data. Compare the results with those of (a).
17.6 Use least-squares regression to fit a straight line to 2 3 4 7 8 1 1.5 2 3 4 8 10 13 (a) Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot the data and the straight line. Assess the fit. (b) Recompute (a), but use polynomial regression to fit a parabola to the data. Compare the results with those of (a).
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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17.6
Transcribed Image Text:* Instead of slope, intercept, and standard error, show the final fitted equation and coefficient of determination (\(R^2\))
** DO repeat the problem with \(x\) and \(y\) reversed and interpret the results.
Transcribed Image Text:### Section 17.6: Using Least-Squares Regression
#### Data Table:
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| y | 1 | 1.5 | 2 | 3 | 4 | 5 | 8 | 10 | 13 |
#### Task:
**(a)** Perform a least-squares regression to fit a straight line to the data points. Calculate the slope and intercept of the line. Determine and compute the standard error of the estimate and the correlation coefficient. Plot the data along with the regression line and evaluate the fit quality.
**(b)** Repeat the analysis conducted in part (a), but this time apply polynomial regression to fit a parabola to the data. Compare these results with those obtained for the linear fit in part (a).
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In the context of educational purposes, these exercises encourage understanding of regression techniques, error analysis, and data fitting, assisting in grasping statistical and analytical concepts in data science and mathematics.
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