### Correlation Between Bills and Tips#### Problem StatementListed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatter plot, find the value of the linear correlation coefficient $ r $, and find the P-value of $ r $. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of $ \alpha = 0.01 $. If everyone were to tip with the same percentage, what should be the value of $ r $?#### Data| Bill (dollars) | 30.46 | 48.91 | 90.03 | 93.68 | 64.35 | 104.74 ||----------------|-------|-------|-------|-------|-------|--------|| Tip (dollars) | 3.59 | 8.21 | 8.36 | 14.33 | 12.70 | 17.38 |#### Instructions1. **Construct a Scatter Plot:** - Plot the given bill amounts on the X-axis. - Plot the corresponding tip amounts on the Y-axis.2. **Calculate the Linear Correlation Coefficient ($ r $):** - Use statistical software or a calculator formula for determining $ r $.3. **Find the P-value of $ r $:** - Again, utilize statistical software or standard statistical tables to determine the P-value for the given $ r $.4. **Interpret the Results:** - Compare the P-value with the significance level $ \alpha = 0.01 $. - Determine if there is sufficient evidence to support a claim of linear correlation between the bill amounts and the tip amounts.#### Hypothetical Scenario- If everyone were to tip with the same percentage, the data points on the scatter plot would lie on a straight line passing through the origin. This would result in a perfect positive linear relationship, and the value of $ r $ should be 1.### Explanation of Graphs or Diagrams- **Scatter Plot:** A graphical representation where each pair of bill and tip amounts is a point plotted on the graph. The X-axis represents the bill amounts, and the Y-axis represents the tip amounts. The patterns and distribution of these points help visualize the relationship between the bill and tip amounts.By following these steps and assessing the values, you can determine

The correlation coefficient is used to measure the linear relation between two variables. There will…

Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 30.46 48.91 3.59 8.21 90.03 93.68 64.35 104.74 O 8.36 14.33 12.70 17,38

Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 30.46 48.91 3.59 8.21 90.03 93.68 64.35 104.74 O 8.36 14.33 12.70 17,38

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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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

### Correlation Between Bills and Tips

#### Problem Statement
Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatter plot, find the value of the linear correlation coefficient $ r $, and find the P-value of $ r $. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of $ \alpha = 0.01 $. If everyone were to tip with the same percentage, what should be the value of $ r $?

#### Data
| Bill (dollars) | 30.46 | 48.91 | 90.03 | 93.68 | 64.35 | 104.74 |
|----------------|-------|-------|-------|-------|-------|--------|
| Tip (dollars) | 3.59 | 8.21 | 8.36 | 14.33 | 12.70 | 17.38 |

#### Instructions
1. **Construct a Scatter Plot:**
- Plot the given bill amounts on the X-axis.
- Plot the corresponding tip amounts on the Y-axis.

2. **Calculate the Linear Correlation Coefficient ($ r $):**
- Use statistical software or a calculator formula for determining $ r $.

3. **Find the P-value of $ r $:**
- Again, utilize statistical software or standard statistical tables to determine the P-value for the given $ r $.

4. **Interpret the Results:**
- Compare the P-value with the significance level $ \alpha = 0.01 $.
- Determine if there is sufficient evidence to support a claim of linear correlation between the bill amounts and the tip amounts.

#### Hypothetical Scenario
- If everyone were to tip with the same percentage, the data points on the scatter plot would lie on a straight line passing through the origin. This would result in a perfect positive linear relationship, and the value of $ r $ should be 1.

### Explanation of Graphs or Diagrams
- **Scatter Plot:** A graphical representation where each pair of bill and tip amounts is a point plotted on the graph. The X-axis represents the bill amounts, and the Y-axis represents the tip amounts. The patterns and distribution of these points help visualize the relationship between the bill and tip amounts.

By following these steps and assessing the values, you can determine

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Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.05. Internet Users 80.6 81.0 57.3 66.8 77.1 38.1 Award Winners 5.3 8.7 3.4 1.7 10.5 0.1
Statistics Question
Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α=0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) 34.14 47.51 85.27 88.36 66.73 105.33 Tip (dollars) 3.51 5.55 16.44 17.42 6.69 13.97
I need help with only the blank boxes that need to be filled in with the answer.
Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.01. If everyone were to tip with the same percentage, what should be the value of r? Bill (dollars) Tip (dollars) 31.80 52.94 85.82 102.16 60.17 111.77 D 5.46 6.07 15.82 15.40 11.15 20.32 Construct a scatterplot. Choose the correct graph below. O A. O B. Oc. D. Q 25- 25- 25 0- 30 0- 30 Bill Amount ($) 0+ 30 Bill Amount (S) 0- 30 Bill Amount (S) 120 120 120 Bill Amount (S) 120 The linear correlation coefficient is r= 0.954 (Round to three decimal places as needed.) Determine the null and alternative hypotheses. Ho: p H,: P (Type integers or decimals. Do not round.) Tip Amount ($) ip Amount ($) Tip Amount ($) Tip Amount ($)
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Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a = 0.05. Internet Users 77.9 79.7 56.2 66.2 78.8 37.6 Award Winners 5.5 8.7 3.3 1.7 10.6 0.1 ..... Construct a scatterplot. Choose the correct graph below. OA. OB. OC. OD. 121 12- 12 12- 30 90 30 Internet Users 30 90 30 90 90 Internet Users Internet Users Internet Users The linear correlation coefficient is r= (Round to three decimal places as needed.) Award Winners Award Winners Award Winners Award Winners
Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a =0.05. Internet Users 79.9 79.4 55.8 67.9 77.3 39.0 Award Winners 5.4 9.1 3.4 1.8 10.6 0.1 Construct a scatterplot. Choose the correct graph below. O A. В. C. D. 12- 12- 12- 12- 0+ 30 0+ 30 0- 30 90 90 30 90 90 Internet Users Internet Users Internet Users Internet Users The linear correlation coefficient is r= (Round to three decimal places as needed.)