Perform correlation and linear regression analysis. 18) A 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. Use a significance level of a = 0.05. Lengths of number one songs (in seconds) Number of weeks the song was number one. 241 224 216 189 163 173 190 218 191 235 125 165 156 201 5 3 5 5 15 3 1 1 2 4 6 3 a) Use the 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) Use Table A-6 to find the critical values for r. c) Determine if there is significant linear correlation in the population. Clearly state the conclusion.

Perform correlation and linear regression analysis. 18) A 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. Use a significance level of a = 0.05. Lengths of number one songs (in seconds) Number of weeks the song was number one. 241 224 216 189 163 173 190 218 191 235 125 165 156 201 5 3 5 5 15 3 1 1 2 4 6 3 a) Use the 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) Use Table A-6 to find the critical values for r. c) Determine if there is significant linear correlation in the population. Clearly state the conclusion.

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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hello this is a two part question im really struggling with it a step by step explantion would really help im so frustrated already with this please i need help.

**Statistical Analysis of Number One Songs**

For the paired data in problem 18 (lengths of number one songs vs. the number of weeks the songs were number one):

1. **Determine the Regression Equation:**
- Identify the regression coefficients $ b_0 $ and $ b_1 $.
- Round $ b_0 $ and $ b_1 $ to three decimal places.

2. **Prediction Analysis:**
- Calculate the best-predicted number of weeks the song will be number one when the length of the number one song is 200 seconds.

This exercise involves analyzing the relationship between the length of songs and their success on the charts. The tools of regression analysis will help you predict the potential success of a song based on its length.

### Perform Correlation and Linear Regression Analysis

A songwriter wants to determine 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. Use a significance level of α = 0.05.

#### Data Table

| Lengths of number one songs (in seconds) | 241 | 224 | 216 | 189 | 163 | 173 | 190 | 218 | 191 | 235 | 125 | 165 | 156 | 201 |
|------------------------------------------|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| Number of weeks the song was number one | 5 | 3 | 5 | 5 | 15 | 3 | 1 | 1 | 2 | 4 | 6 | 3 | 1 | 6 |

### Tasks

a) Use the 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) Use Table A-6 to find the critical values for $ r $.

c) Determine if there is significant linear correlation in the population. Clearly state the conclusion.

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