**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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