### Exercise: Analyzing the CorrelationIn this exercise, we will learn how to analyze the correlation between two datasets using a calculator and interpret the results. Follow the steps below:#### a) Calculate the Correlation Coefficient (r)Use your calculator to find the correlation coefficient \( r \) between the lengths of number one songs and the number of weeks the songs were number one.#### b) Determine Critical Values from Table A-6Refer to Table A-6 to find the critical values for \( r \). This table provides thresholds to help interpret the strength and significance of the correlation.#### c) Analyze Linear CorrelationAfter calculating the correlation coefficient and referring to the critical values, determine if there is a significant linear correlation in the population. Clearly state your conclusion based on the analysis.#### Detailed Instructions1. **Using the Calculator**: - Input the data for the lengths of the songs and the number of weeks at number one. - Calculate \( r \) which measures the strength and direction of the linear relationship between the two variables.2. **Using Table A-6**: - Look for the specific degrees of freedom associated with your dataset (number of pairs of data points - 2). - Identify the critical value for \( r \) which will let you determine whether your calculated \( r \) is statistically significant.3. **Conclusion**: - Compare your calculated \( r \) with the critical value from Table A-6. - State whether the correlation is significant. If \( r \) exceeds the critical value, there is a significant correlation; otherwise, it is not significant.This exercise helps in understanding how to determine the strength and significance of the relationship between two quantitative variables. ### Perform Correlation and Linear Regression Analysis#### Problem StatementA songwriter wants to know if there is a correlation between the length of a number one song in recent years and the number of weeks the song was number one. The following table lists the lengths (in seconds) of randomly selected number one songs and the number of weeks the songs were number one in recent years. The analysis should be performed using a significance level of α = 0.05.#### Data TableThe table below provides data on the lengths of number one songs and the number of weeks they remained at number one:| Lengths of number one songs (in seconds) | 222 | 411 | 116 | 379 | 119 | 321 | 116 | 366 | 508 | 146 | 993 | 338 | 308 | 815 | 155 | 561 ||------------------------------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|| Number of weeks the song was number one | 5 | 3 | 5 | 5 | 1 | 3 | 1 | 1 | 2 | 4 | 6 | 3 | 1 | 6 | 3 | 1 |#### InstructionsTo determine if there is a significant correlation between the length of a song and the number of weeks it stays at number one, you need to:1. Calculate the correlation coefficient between the lengths of the songs and the number of weeks they were number one.2. Perform a linear regression analysis to find the best-fit line for the data.3. Determine if the correlation is statistically significant using the given significance level of α = 0.05.Use appropriate statistical software or tools to perform these calculations and draw conclusions based on the results.

The data for lengths of the number one song and the number of weeks the song was number one is…

Answered: a) Use the calculator to find the…

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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This question has 6 parts, Thank you.
Please Answer Questions A through C. Correlation table is provided.
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