please show all work and please organize answers to questions in order so it’s not difficult to understand **Scatter Diagram and Correlation Analysis**Below is a scatter diagram for variables \( x \) and \( y \). The sample correlation coefficient for the data is \( r = -0.823 \).**Scatter Diagram Description:**The scatter diagram consists of several plotted points that represent paired values of \( x \) and \( y \). The \( x \)-axis ranges from 0 to 35, while the \( y \)-axis ranges from 0 to 100. The points appear to follow a downward trend, suggesting a possible negative relationship between the two variables.**Questions for Analysis:**1. **Is there a linear correlation between \( x \) and \( y \)?** - Use the "Critical Values for Correlation Coefficient" table provided to justify your answer.2. **If there is linear correlation, is it positive or negative?**Based on the given information, since \( r = -0.823 \), it indicates a strong negative linear correlation between \( x \) and \( y \). ### Critical Values for Correlation CoefficientThe table below provides the critical values for the correlation coefficient. These values are essential for determining the statistical significance of a correlation in hypothesis testing. The column labeled "n" represents the sample size, while the adjacent numbers indicate the critical correlation coefficients for that particular sample size.| n | Coefficient | n | Coefficient | n | Coefficient | n | Coefficient ||----|-------------|----|-------------|----|-------------|----|-------------|| 3 | 0.997 | 10 | 0.632 | 17 | 0.482 | 24 | 0.404 || 4 | 0.950 | 11 | 0.602 | 18 | 0.468 | 25 | 0.396 || 5 | 0.878 | 12 | 0.576 | 19 | 0.456 | 26 | 0.388 || 6 | 0.811 | 13 | 0.553 | 20 | 0.444 | 27 | 0.381 || 7 | 0.754 | 14 | 0.532 | 21 | 0.433 | 28 | 0.374 || 8 | 0.707 | 15 | 0.514 | 22 | 0.423 | 29 | 0.367 || 9 | 0.666 | 16 | 0.497 | 23 | 0.413 | 30 | 0.361 |#### Explanation:- **Sample Size (n):** This is the number of paired observations.- **Critical Value of Correlation Coefficient:** The smallest value for the correlation coefficient that can be considered statistically significant at a given significance level, typically 0.05.This table is utilized in statistical analysis to determine if the observed correlation in a sample is significantly different from zero at a certain significance level.

Below a scatter diagram for x and y. The sample correlation coefficient for the data r = -0.823. 100 90 80 70 60 <-50 40 30 20 10 0 5 10 15 20 25 30 35 Is there a linear correlation between x and y? Use the "Critical Values for Correlation Coefficient" table provided to justify your answer. If there is linear correlation, is it positive or negative?

Below a scatter diagram for x and y. The sample correlation coefficient for the data r = -0.823. 100 90 80 70 60 <-50 40 30 20 10 0 5 10 15 20 25 30 35 Is there a linear correlation between x and y? Use the "Critical Values for Correlation Coefficient" table provided to justify your answer. If there is linear correlation, is it positive or negative?

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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