**Title: Understanding Scatterplots and Correlation Coefficients****Section 10.1.4: Scatterplots****Objective:**Learn how to match values of correlation coefficient $ r $ with corresponding scatterplots.**Task:**Match the given values of $ r $ to the appropriate scatterplots.**Scatterplots Overview:**There are five scatterplots presented, labeled Scatterplot 1 to Scatterplot 5. Each scatterplot displays a set of data points on a two-dimensional graph, helping visualize the correlation between two variables $ x $ and $ y $.**Scatterplot Descriptions:**1. **Scatterplot 4:** - Data Points: Arranged in a positive linear trend on the graph. - Axes Range: The x-axis ranges from 0.2 to 1, and the y-axis shows a corresponding upward trend. 2. **Scatterplot 5:** - Data Points: Also show a positive linear trend. - Axes: The x-axis and y-axis are similarly structured as Scatterplot 4, reinforcing a positive correlation. 3. **Additional Scatterplot (right panel):** - Data Points: Appear to be scattered with a downward trend. - Axes: The x-axis ranges are similar, indicating a negative correlation.**Instructions:**- Use the drop-down menus next to each scatterplot label to select the corresponding correlation coefficient $ r $. - Evaluate the direction and strength of the linear relationship depicted in each scatterplot to determine the value of $ r $.**Interactive Features:**- Icons next to each scatterplot allow you to zoom in for better examination.- Scroll and navigate between different scatterplots if needed.**Final Steps:**Once you match the scatterplots with the appropriate correlation coefficients, click ‘Done’ to finalize your answers.**Note:**Understanding the correlation coefficient:- $ r = 1 $ indicates a perfect positive linear relationship.- $ r = -1 $ indicates a perfect negative linear relationship.- $ r = 0 $ indicates no linear relationship.This understanding will assist in evaluating the scatterplots more efficiently. **Interactive Exercise: Matching Correlation Coefficients with Scatterplots**In this exercise, you will match correlation coefficients (r) with corresponding scatterplots. The values of the correlation coefficients provided are: 0.998, -0.998, 0.369, -0.369, and 1.For each scatterplot listed below, use the drop-down menu to select the correct value of r that best matches the relationship displayed in the scatterplot.- **Scatterplot 1, r =** [Select]- **Scatterplot 2, r =** [Select]- **Scatterplot 3, r =** [Select]- **Scatterplot 4, r =** [Select]- **Scatterplot 5, r =** [Select]**Instructions:**1. Click to select your answer(s) for each scatterplot.2. Once you have selected your answers, click "Check Answer" to verify your choices.Remember:- A correlation close to 1 indicates a strong positive linear relationship.- A correlation close to -1 signifies a strong negative linear relationship.- A correlation around 0 suggests little to no linear relationship.**Note:** Diagrams and graphs would typically show data points arranged in various patterns that exhibit the described relationships, but are not visible in this transcription.

Scatter plot 1, r = 1 since, it shows a perfect straight line pattern the value of r is 1. Scatter plot 2, r = 0.998 Since, it has a straight line pattern but not perfect the value of r is 0.998.Scatter plot 3, r = -0.998 Since, it has a downhill straight line pattern the value of r is -0.998. Scatter plot 4, r = -0.369 Since, it has downhill pattern with points scattered away the value of r is -0.369.Scatter plot 5, r = 0.369 Since, it has uphill pattern with points scattered away the value of r is 0.369.

Math

Statistics

Match these values of r with the ac W Click the icon to view the scat 2 Match the values of r to the scatter 6 -4- 4 Scatterplot 1, r= 6- 2- Scatterplot 2, r= 0- 0.2 0.4 0.6 08 Scatterplot 3, r= 02 04 0. 6 08 0.2 0.4 0.6 08 1 Scatterplot 4, r= Scatterplot 4 Scatterplot 5 Scatterplot 5, r= 8- 6-

Match these values of r with the ac W Click the icon to view the scat 2 Match the values of r to the scatter 6 -4- 4 Scatterplot 1, r= 6- 2- Scatterplot 2, r= 0- 0.2 0.4 0.6 08 Scatterplot 3, r= 02 04 0. 6 08 0.2 0.4 0.6 08 1 Scatterplot 4, r= Scatterplot 4 Scatterplot 5 Scatterplot 5, r= 8- 6-

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

100%

**Title: Understanding Scatterplots and Correlation Coefficients**

**Section 10.1.4: Scatterplots**

**Objective:**
Learn how to match values of correlation coefficient $ r $ with corresponding scatterplots.

**Task:**
Match the given values of $ r $ to the appropriate scatterplots.

**Scatterplots Overview:**
There are five scatterplots presented, labeled Scatterplot 1 to Scatterplot 5. Each scatterplot displays a set of data points on a two-dimensional graph, helping visualize the correlation between two variables $ x $ and $ y $.

**Scatterplot Descriptions:**

1. **Scatterplot 4:**
- Data Points: Arranged in a positive linear trend on the graph.
- Axes Range: The x-axis ranges from 0.2 to 1, and the y-axis shows a corresponding upward trend.

2. **Scatterplot 5:**
- Data Points: Also show a positive linear trend.
- Axes: The x-axis and y-axis are similarly structured as Scatterplot 4, reinforcing a positive correlation.

3. **Additional Scatterplot (right panel):**
- Data Points: Appear to be scattered with a downward trend.
- Axes: The x-axis ranges are similar, indicating a negative correlation.

**Instructions:**
- Use the drop-down menus next to each scatterplot label to select the corresponding correlation coefficient $ r $.
- Evaluate the direction and strength of the linear relationship depicted in each scatterplot to determine the value of $ r $.

**Interactive Features:**
- Icons next to each scatterplot allow you to zoom in for better examination.
- Scroll and navigate between different scatterplots if needed.

**Final Steps:**
Once you match the scatterplots with the appropriate correlation coefficients, click ‘Done’ to finalize your answers.

**Note:**
Understanding the correlation coefficient:
- $ r = 1 $ indicates a perfect positive linear relationship.
- $ r = -1 $ indicates a perfect negative linear relationship.
- $ r = 0 $ indicates no linear relationship.

This understanding will assist in evaluating the scatterplots more efficiently.

**Interactive Exercise: Matching Correlation Coefficients with Scatterplots**

In this exercise, you will match correlation coefficients (r) with corresponding scatterplots. The values of the correlation coefficients provided are: 0.998, -0.998, 0.369, -0.369, and 1.

For each scatterplot listed below, use the drop-down menu to select the correct value of r that best matches the relationship displayed in the scatterplot.

- **Scatterplot 1, r =** [Select]
- **Scatterplot 2, r =** [Select]
- **Scatterplot 3, r =** [Select]
- **Scatterplot 4, r =** [Select]
- **Scatterplot 5, r =** [Select]

**Instructions:**
1. Click to select your answer(s) for each scatterplot.
2. Once you have selected your answers, click "Check Answer" to verify your choices.

Remember:
- A correlation close to 1 indicates a strong positive linear relationship.
- A correlation close to -1 signifies a strong negative linear relationship.
- A correlation around 0 suggests little to no linear relationship.

**Note:** Diagrams and graphs would typically show data points arranged in various patterns that exhibit the described relationships, but are not visible in this transcription.

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