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MATLAB: An Introduction with Applications

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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Question

**Bivariate Data Analysis**

The following table presents bivariate data for the quantitative variables \( x \) and \( y \). A scatter plot of this data is displayed next to the table, illustrating the relationship between the two variables.

**Data Table:**

| \( x \) | \( y \) |
|--------|--------|
| 7.5 | 8.8 |
| 2.9 | 1.8 |
| 3.4 | 3.4 |
| 5.7 | 4.7 |
| 3.2 | 2.9 |
| 4.0 | 1.7 |
| 4.4 | 3.5 |
| 5.2 | 3.6 |
| 6.8 | 6.5 |
| 8.5 | 9.5 |
| 4.5 | 4.4 |
| 5.8 | 7.3 |
| 6.7 | 6.9 |
| 10.6 | 8.8 |
| 7.5 | 7.6 |
| 8.1 | 9.6 |
| 5.6 | 4.4 |
| 8.7 | 9.8 |
| 6.4 | 5.2 |

**Scatter Plot Explanation:**

- The scatter plot is a graphical representation of the data with \( x \)-axis representing the variable \( x \) and the \( y \)-axis representing the variable \( y \).
- Each point on the plot corresponds to a pair of values \( (x, y) \) from the table.
- Observing the scatter plot, there appears to be a positive correlation between \( x \) and \( y \), meaning as \( x \) increases, \( y \) tends to increase as well.
- To better understand this relationship, one can sketch an approximation of the least-squares regression line, which minimizes the distance between the data points and the line itself.

You are encouraged to draw the least-squares regression line on the scatter plot to visually assess the strength and nature of the relationship between these variables.

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