**Regression Analysis with Outliers: Understanding Correlation**A student uses the following dataset to compute a least-squares regression line and determine the correlation coefficient:\[\begin{array}{c|ccccccc}x & 0.7 & 0.8 & 1.7 & 1.7 & 1.3 & 2.6 & 8.0 \\\hliney & 1 & 2 & 2 & 1 & 0 & 1 & 5 \\\end{array}\]The student's task is to evaluate whether the regression line effectively illustrates the relationship between the explanatory variable \(x\) and the response variable \(y\).### Evaluation Question:Is the student's claim correct that the regression line provides an excellent explanation of the relationship?### Response Options:- **Option 1:** - **No,** because the outlier is inflating the correlation coefficient.- **Option 2:** - **No,** because the slope of the regression line is only 0.54.- **Option 3:** - **Yes,** because \( r^2 = 0.74 \) means that 74% of the variation in \( y \) is explained by the least-squares regression of \( y \) on \( x \).- **Option 4:** - **Yes,** because the correlation coefficient is \( r = 0.86 \), which is close to 1.### Discussion:The key points to consider include the impact of outliers on the correlation coefficient, the significance of the slope in describing the fit of the regression line, and the interpretations of \( r^2 \) and \( r \).

Here, sample size 'n' is 7. The linear regression line is given by: x y x2 y2 xy 0.7 1 0.49 1…

A student uses the given set of data to compute a least-squares regression line and a correlation coefficient: 0.7 0.8 1.7 1.7 1.3 2.6 8.0 y 1 2 1 1 5 The student claims that the regression line does an excellent job of explaining the relationship between the explanatory variable x and the response variable y. Is the student correct? No, because the outlier is inflating the correlation coefficient. No, because the slope of the regression line is only 0.54. Yes, because r2 = 0.74 means that 74% of the variation in y is explained by the least-squares regression of y on x. Yes, because the correlation coefficient is r = 0.86, which is close to 1. 2.

A student uses the given set of data to compute a least-squares regression line and a correlation coefficient: 0.7 0.8 1.7 1.7 1.3 2.6 8.0 y 1 2 1 1 5 The student claims that the regression line does an excellent job of explaining the relationship between the explanatory variable x and the response variable y. Is the student correct? No, because the outlier is inflating the correlation coefficient. No, because the slope of the regression line is only 0.54. Yes, because r2 = 0.74 means that 74% of the variation in y is explained by the least-squares regression of y on x. Yes, because the correlation coefficient is r = 0.86, which is close to 1. 2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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