Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as y = - 51.77x + 40.56 and the r = - 0.9. What percentage of the variation in y can be explained by the variation in the values of x? * (Report exact answer, and do not enter the % sign) Submit Question

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as 

\[ y = -51.77x + 40.56 \]

and the correlation coefficient \( r = -0.9 \).

What percentage of the variation in \( y \) can be explained by the variation in the values of \( x \)?

\[ r^2 = \_\_\_\_ \] % (Report exact answer, and do not enter the % sign)

[Submit Question]

**Explanation:**

In this problem, you're asked to find the coefficient of determination (\( r^2 \)), which tells you what percentage of the variation in the dependent variable \( y \) is explained by the independent variable \( x \). Given that the correlation coefficient \( (r) \) is \(-0.9\), calculate \( r^2 \) as follows:

\[ r^2 = (-0.9)^2 = 0.81 \]

Thus, 81% of the variation in \( y \) is explained by the variation in \( x \). Enter the value of \( r^2 \) in the provided space without the percentage sign, as instructed.
Transcribed Image Text:Using your favorite statistics software package, you generate a scatter plot with a regression equation and correlation coefficient. The regression equation is reported as \[ y = -51.77x + 40.56 \] and the correlation coefficient \( r = -0.9 \). What percentage of the variation in \( y \) can be explained by the variation in the values of \( x \)? \[ r^2 = \_\_\_\_ \] % (Report exact answer, and do not enter the % sign) [Submit Question] **Explanation:** In this problem, you're asked to find the coefficient of determination (\( r^2 \)), which tells you what percentage of the variation in the dependent variable \( y \) is explained by the independent variable \( x \). Given that the correlation coefficient \( (r) \) is \(-0.9\), calculate \( r^2 \) as follows: \[ r^2 = (-0.9)^2 = 0.81 \] Thus, 81% of the variation in \( y \) is explained by the variation in \( x \). Enter the value of \( r^2 \) in the provided space without the percentage sign, as instructed.
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