**Title**: Understanding Scatter Diagrams and Relationships Between Variables**Introduction**: In this lesson, we will analyze a dataset representing the percentage of a country’s population aged 20 years or older who do not have a high school diploma. We will explore how to use scatter diagrams to visualize data and determine the type of relationship between age and the percentage of the population without a high school diploma.**Dataset**:The table below provides data on the age and corresponding percentage of the population without a high school diploma:| Age, a | 20 | 30 | 40 | 50 | 60 | 70 ||--------|-----|-----|-----|-----|-----|-----|| Percentage without a H.S. Diploma, P | 13.1 | 11.5 | 10.5 | 13.5 | 22.3 | 29.8 |**Task**:(a) Using a graphing utility, draw a scatter diagram of the data treating age as the independent variable. What type of relation appears to exist between age and percentage of the population without a high school diploma?**Question**:*Which graph below is a scatter diagram of the data?*The four options for scatter diagrams are labeled as A, B, C, and D.- **Option A**: This scatter diagram shows points that trend upwards, suggesting a possible relationship where the percentage increases with age.- **Option B**: This scatter diagram shows points scattered randomly without any clear trend, suggesting no discernible relationship between age and percentage.- **Option C**: This scatter diagram shows points forming a quadratic pattern, suggesting a non-linear relationship where the percentage first decreases then increases with age.- **Option D**: This scatter diagram shows points forming a quadratic pattern but with age and percentage axes reversed.**Analysis**:To determine which option best represents the data, compare each scatter diagram to the values in the table.1. **Option A** shows a clear upward trend as age increases, which suggests an increasing percentage of the population without a high school diploma with age.2. **Option B** doesn't show any clear relationship, which contradicts the data pattern.3. **Option C** shows a U-shaped quadratic trend, which could represent the pattern seen in the table where percentages decrease initially and then increase.4. **Option D** has axes reversed, which doesn't correspond correctly to the task. ### Educational Content - Relationship Between Age and Percentage of Population Without a High School Diploma#### Part (a): Analyzing the Relation Between Age and Percentage**Question:** Use the graph to determine which sentence below best describes the relation between age and the percentage of the population without a high school diploma.**Options:**- **A.** There appears to be a linear relation between age and percentage.- **B.** There does not appear to be any relation between age and percentage.- **C.** There appears to be a quadratic relation between age and percentage.#### Part (b): Identifying the Equation**Question:** Based on your response to part (a), find either a linear or quadratic model that describes the relation between age and percentage of the population that do not have a high school diploma.**Options:**- **A.** $ P = 0.015a + 27.713 $- **B.** $ P = -1.022a^2 + 0.015a + 1.496 $- **C.** $ P = 1.496a + 0.34 $- **D.** $ P = 0.015a^2 - 1.022a + 27.713 $- **E.** $ P = 0.34a^2 + 1.496 $- **F.** $ P = 0.34a + 1.496 $- **G.** There is no relation.#### Part (c): Prediction Using the Model**Question:** Use the model you selected in part (b) to predict the percentage of 75-year-olds that do not have a high school diploma.**Instruction:** The predicted percentage of 75-year-olds that do not have a high school diploma is about \[ \text{ } \]%.(Use the answer from part (b) to find this answer. Round to the nearest whole number as needed.)#### How to Use the GraphThe graph provides a visual representation of the relationship between age and the percentage of the population without a high school diploma. Analyzing the graph will help in selecting the correct model (linear or quadratic) and equation from the options provided.### Understanding Graphs and ModelsGraphs can illustrate trends and patterns within data, and selecting the correct model (linear or quadratic) can aid in predictions and understanding relationships within

In regression, a best line is fitted in the data to make predictions about the known values of…

The data in the table below represents the percentage of a country's population aged 20 years or older whose age is x who do not have a high school diploma. Complete parts (a) through (c) below. 50 Age, a Pecentage without a H. S. Diploma, P 20 30 40 60 70 13.1 11.5 10.5 13.5 22.3 29.8 (a) Using a graphing utility, draw a scatter diagram of the data treating age as the independent variable. What type of relation appears to exist between age and percentage of the population without a high school diploma? Which graph below is a scatter diagram of the data? O A. OB. Oc. OD. 70- 404 70- 40- Use the graph to determine which sentence below best describes the relation between age and percentage of the population without a high school diploma. O A. There appearst be a linear relation between age and percentage. O B. There does not appear to be any relation between age and percentage. OC. There appears to be a quadratic relation between age and percentage.

The data in the table below represents the percentage of a country's population aged 20 years or older whose age is x who do not have a high school diploma. Complete parts (a) through (c) below. 50 Age, a Pecentage without a H. S. Diploma, P 20 30 40 60 70 13.1 11.5 10.5 13.5 22.3 29.8 (a) Using a graphing utility, draw a scatter diagram of the data treating age as the independent variable. What type of relation appears to exist between age and percentage of the population without a high school diploma? Which graph below is a scatter diagram of the data? O A. OB. Oc. OD. 70- 404 70- 40- Use the graph to determine which sentence below best describes the relation between age and percentage of the population without a high school diploma. O A. There appearst be a linear relation between age and percentage. O B. There does not appear to be any relation between age and percentage. OC. There appears to be a quadratic relation between age and percentage.

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

**Title**: Understanding Scatter Diagrams and Relationships Between Variables

**Introduction**: In this lesson, we will analyze a dataset representing the percentage of a country’s population aged 20 years or older who do not have a high school diploma. We will explore how to use scatter diagrams to visualize data and determine the type of relationship between age and the percentage of the population without a high school diploma.

**Dataset**:
The table below provides data on the age and corresponding percentage of the population without a high school diploma:

| Age, a | 20 | 30 | 40 | 50 | 60 | 70 |
|--------|-----|-----|-----|-----|-----|-----|
| Percentage without a H.S. Diploma, P | 13.1 | 11.5 | 10.5 | 13.5 | 22.3 | 29.8 |

**Task**:
(a) Using a graphing utility, draw a scatter diagram of the data treating age as the independent variable. What type of relation appears to exist between age and percentage of the population without a high school diploma?

**Question**:
*Which graph below is a scatter diagram of the data?*

The four options for scatter diagrams are labeled as A, B, C, and D.

- **Option A**: This scatter diagram shows points that trend upwards, suggesting a possible relationship where the percentage increases with age.
- **Option B**: This scatter diagram shows points scattered randomly without any clear trend, suggesting no discernible relationship between age and percentage.
- **Option C**: This scatter diagram shows points forming a quadratic pattern, suggesting a non-linear relationship where the percentage first decreases then increases with age.
- **Option D**: This scatter diagram shows points forming a quadratic pattern but with age and percentage axes reversed.

**Analysis**:
To determine which option best represents the data, compare each scatter diagram to the values in the table.

1. **Option A** shows a clear upward trend as age increases, which suggests an increasing percentage of the population without a high school diploma with age.
2. **Option B** doesn't show any clear relationship, which contradicts the data pattern.
3. **Option C** shows a U-shaped quadratic trend, which could represent the pattern seen in the table where percentages decrease initially and then increase.
4. **Option D** has axes reversed, which doesn't correspond correctly to the task.

### Educational Content - Relationship Between Age and Percentage of Population Without a High School Diploma

#### Part (a): Analyzing the Relation Between Age and Percentage
**Question:** Use the graph to determine which sentence below best describes the relation between age and the percentage of the population without a high school diploma.

**Options:**
- **A.** There appears to be a linear relation between age and percentage.
- **B.** There does not appear to be any relation between age and percentage.
- **C.** There appears to be a quadratic relation between age and percentage.

#### Part (b): Identifying the Equation
**Question:** Based on your response to part (a), find either a linear or quadratic model that describes the relation between age and percentage of the population that do not have a high school diploma.

**Options:**
- **A.** $ P = 0.015a + 27.713 $
- **B.** $ P = -1.022a^2 + 0.015a + 1.496 $
- **C.** $ P = 1.496a + 0.34 $
- **D.** $ P = 0.015a^2 - 1.022a + 27.713 $
- **E.** $ P = 0.34a^2 + 1.496 $
- **F.** $ P = 0.34a + 1.496 $
- **G.** There is no relation.

#### Part (c): Prediction Using the Model
**Question:** Use the model you selected in part (b) to predict the percentage of 75-year-olds that do not have a high school diploma.

**Instruction:** The predicted percentage of 75-year-olds that do not have a high school diploma is about \[ \text{ } \]%.

(Use the answer from part (b) to find this answer. Round to the nearest whole number as needed.)

#### How to Use the Graph
The graph provides a visual representation of the relationship between age and the percentage of the population without a high school diploma. Analyzing the graph will help in selecting the correct model (linear or quadratic) and equation from the options provided.

### Understanding Graphs and Models
Graphs can illustrate trends and patterns within data, and selecting the correct model (linear or quadratic) can aid in predictions and understanding relationships within

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