### Understanding the Linear Correlation Coefficient (r)The variable \( r \) is known as the linear correlation coefficient. It quantifies the strength and direction of a linear relationship between two variables in a scatter plot. The \( r \) value ranges from -1 to 1, where:- \( r = 1 \): Perfect positive linear correlation.- \( r = -1 \): Perfect negative linear correlation.- \( r = 0 \): No linear correlation.### Analysis of Scatter Plots Based on \( r \) Values#### Scatter Plot Data- **Graph 1: \( r = -0.87 \)**- **Graph 2: \( r = 0.58 \)**- **Graph 3: \( r = 0.09 \)**#### Interpretation of \( r \) Values1. **Graph 1 ( \( r = -0.87 \) )**: - **Correlation Type**: Strong negative correlation. - **Description**: As one variable increases, the other variable tends to decrease significantly. The scatter plot will show data points closely aligned along a downward-sloping line.2. **Graph 2 ( \( r = 0.58 \) )**: - **Correlation Type**: Moderate positive correlation. - **Description**: As one variable increases, the other variable tends to increase as well, but the correlation is not perfect. The scatter plot will show data points forming a somewhat loose upward-sloping pattern.3. **Graph 3 ( \( r = 0.09 \) )**: - **Correlation Type**: Very weak positive correlation. - **Description**: There is hardly any noticeable linear relationship between the two variables. The scatter plot will show data points scattered loosely with no discernible pattern.Understanding these \( r \) values helps in interpreting the relationship between the variables and provides insight into how strongly they are associated with each other.

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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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Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axes are the same for each diagram. (a) r= - (b) r= - 0.546 0.025 0.946 (c) r= - (d) r= - 1 Click the icon to view the scatter diagrams. ..... r= - 0.025 r= - 0.546 r= - 0.946 r= - 1 Drag each of the r-values given above into the appropriate area below. Explanatory Explanatory Explanatory Explanatory Response Response Response Response • .
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Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axes are the same for each diagram. (a) r= 0.523 (b) r= - 0.969 (c) r= 0.025 (d) r= 1 Click the icon to view the scatter diagrams. r= 1 r= 0.523 r= - 0.969 r= 0.025 Drag each of the r-values given above into the appropriate area below. Explanatory Explanatory Explanatory Explanatory Response Response Response Response

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The variable ris known as the linear correlation coefficient. Summarize what the rvalue tells you about the scatter plot. What type of correlation will the follow scatter plots have based on the r values? Scatter r Values Plots Graph 1 r=-0.87 Graph 2 r= 0.58 Graph 3 r= 0.09