### Analysis of the Relationship Between Educational Attainment and Annual SalaryA social scientist aims to study the correlation between years of higher education and annual salary in thousands of dollars. Data has been collected from 20 individuals, with a sample displayed below:| Salary | Education ||--------|-----------|| 34 | 3 || 66 | 1 || ... | ... || 33 | 0 |#### Data File- [Click here for the Excel Data File](#)#### Task A: Construct the Regression EquationFind the sample regression equation in the form: \[ \text{Salary} = \beta_0 + \beta_1 \times \text{Education} + \varepsilon \]Round your answers to two decimal places.#### Task B: Interpret the Coefficient for EducationChoose the correct interpretation:- As Education increases by 1 year, an individual’s annual salary is predicted to increase by $4,690.- As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $8,590.- As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $4,690.- As Education increases by 1 year, an individual’s annual salary is predicted to increase by $8,590.#### Task C: Salary PredictionCalculate the predicted salary for an individual with 7 years of higher education. Round the coefficient estimates to at least 4 decimal places and the answer to the nearest whole number.\[ \text{Salary} = \$ \_\_\_\_ \]This exercise illustrates the application of linear regression to understand the impact of educational attainment on salary, an essential analysis in social sciences and economics. The table displayed contains two columns, "Salary" and "Education," with each row representing a distinct data entry. The "Salary" column provides numerical values representing salary figures, while the "Education" column contains numerical values that could represent levels of education completed.Here is a transcription of the data:| Salary | Education ||--------|-----------|| 34 | 3 || 66 | 1 || 89 | 4 || 56 | 3 || 71 | 7 || 80 | 2 || 111 | 7 || 51 | 0 || 23 | 7 || 36 | 2 || 100 | 1 || 35 | 1 || 71 | 6 || 68 | 9 || 163 | 5 || 56 | 0 || 86 | 5 || 58 | 4 || 128 | 9 || 33 | 0 |This data could be utilized for analyzing the correlation between salary levels and education attainment, though the specifics of educational levels are not defined here.

Answered: Image /qna-images/answer/61199035-e774-4cd3-8afd-81f986783b6f.jpg

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary 34 Education 3 66 1 33 Click here for the Excel Data File a. Find the sample regression equation for the model: Salary = Bo + B1Education + ɛ. (Round answers to 2 decimal places.) Salary Education b. Interpret the coefficient for Education. O As Education increases by 1 year, an individual's annual salary is predicted to increase by $4,690. O As Education increases by 1 year, an individual's annual salary is predicted to decrease by $8,590. O As Education increases by 1 year, an individual's annual salary is predicted to decrease by $4,690. O As Education increases by 1 year, an individual's annual salary is predicted to increase by $8,590. c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.) Salary

A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows: Salary 34 Education 3 66 1 33 Click here for the Excel Data File a. Find the sample regression equation for the model: Salary = Bo + B1Education + ɛ. (Round answers to 2 decimal places.) Salary Education b. Interpret the coefficient for Education. O As Education increases by 1 year, an individual's annual salary is predicted to increase by $4,690. O As Education increases by 1 year, an individual's annual salary is predicted to decrease by $8,590. O As Education increases by 1 year, an individual's annual salary is predicted to decrease by $4,690. O As Education increases by 1 year, an individual's annual salary is predicted to increase by $8,590. c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.) Salary

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6th Edition

ISBN:9781119256830

Author:Amos Gilat

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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

### Analysis of the Relationship Between Educational Attainment and Annual Salary

A social scientist aims to study the correlation between years of higher education and annual salary in thousands of dollars. Data has been collected from 20 individuals, with a sample displayed below:

| Salary | Education |
|--------|-----------|
| 34 | 3 |
| 66 | 1 |
| ... | ... |
| 33 | 0 |

#### Data File
- [Click here for the Excel Data File](#)

#### Task A: Construct the Regression Equation
Find the sample regression equation in the form:
\[ \text{Salary} = \beta_0 + \beta_1 \times \text{Education} + \varepsilon \]
Round your answers to two decimal places.

#### Task B: Interpret the Coefficient for Education
Choose the correct interpretation:
- As Education increases by 1 year, an individual’s annual salary is predicted to increase by $4,690.
- As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $8,590.
- As Education increases by 1 year, an individual’s annual salary is predicted to decrease by $4,690.
- As Education increases by 1 year, an individual’s annual salary is predicted to increase by $8,590.

#### Task C: Salary Prediction
Calculate the predicted salary for an individual with 7 years of higher education. Round the coefficient estimates to at least 4 decimal places and the answer to the nearest whole number.

\[ \text{Salary} = \$ \_\_\_\_ \]

This exercise illustrates the application of linear regression to understand the impact of educational attainment on salary, an essential analysis in social sciences and economics.

The table displayed contains two columns, "Salary" and "Education," with each row representing a distinct data entry. The "Salary" column provides numerical values representing salary figures, while the "Education" column contains numerical values that could represent levels of education completed.

Here is a transcription of the data:

| Salary | Education |
|--------|-----------|
| 34 | 3 |
| 66 | 1 |
| 89 | 4 |
| 56 | 3 |
| 71 | 7 |
| 80 | 2 |
| 111 | 7 |
| 51 | 0 |
| 23 | 7 |
| 36 | 2 |
| 100 | 1 |
| 35 | 1 |
| 71 | 6 |
| 68 | 9 |
| 163 | 5 |
| 56 | 0 |
| 86 | 5 |
| 58 | 4 |
| 128 | 9 |
| 33 | 0 |

This data could be utilized for analyzing the correlation between salary levels and education attainment, though the specifics of educational levels are not defined here.

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