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What percentage of the variation of income is explained by education? Do not use decimal place, round and input whole integer percentage such as x or xx. So if answer is 58.3% then you would input 58.

What percentage of the variation of income is explained by education? Do not use decimal place, round and input whole integer percentage such as x or xx. So if answer is 58.3% then you would input 58.

MATLAB: An Introduction with Applications
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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### Analysis of the Relationship between Education and Income in California A survey was conducted on 700 Californians older than 30 years of age. The purpose of this study is to understand the relationship between years of education and yearly income in dollars. The response variable is income in dollars and the explanatory variable is years of education. A simple linear regression model was fitted to the data, and the output from R is provided below: ```R lm(formula = Income ~ Education, data = CA) ``` #### Coefficients: | | Estimate | Std. Error | t value | Pr(>|t|) | |--------------|------------|------------|---------|----------:| | (Intercept) | 25200.25 | 1488.94 | 16.93 | 3.08e-10 *** | | Education | 2905.35 | 112.61 | 25.80 | 1.49e-12 *** | #### Additional Model Information: - **Residual standard error**: 32400 on 698 degrees of freedom - **Multiple R-squared**: 0.7602 ### Explanation: - **Intercept (25200.25)**: This indicates that the base income, when the years of education is zero, is $25,200.25. - **Education Coefficient (2905.35)**: This estimate suggests that each additional year of education is associated with an increase in income by $2,905.35. - **Pr(>|t|) Values and Significance Levels**: Both coefficients (Intercept and Education) are highly significant, as indicated by the very small p-values (3.08e-10 and 1.49e-12) which are less than 0.001, denoted by the triple asterisks (***). - **Residual Standard Error (32400)**: The average amount that a response will deviate from the true regression line. - **Multiple R-squared (0.7602)**: This value indicates that approximately 76.02% of the variability in annual income can be explained by the years of education. This regression model demonstrates a strong positive relationship between years of education and annual income among the surveyed Californians.
Transcribed Image Text:### Analysis of the Relationship between Education and Income in California A survey was conducted on 700 Californians older than 30 years of age. The purpose of this study is to understand the relationship between years of education and yearly income in dollars. The response variable is income in dollars and the explanatory variable is years of education. A simple linear regression model was fitted to the data, and the output from R is provided below: ```R lm(formula = Income ~ Education, data = CA) ``` #### Coefficients: | | Estimate | Std. Error | t value | Pr(>|t|) | |--------------|------------|------------|---------|----------:| | (Intercept) | 25200.25 | 1488.94 | 16.93 | 3.08e-10 *** | | Education | 2905.35 | 112.61 | 25.80 | 1.49e-12 *** | #### Additional Model Information: - **Residual standard error**: 32400 on 698 degrees of freedom - **Multiple R-squared**: 0.7602 ### Explanation: - **Intercept (25200.25)**: This indicates that the base income, when the years of education is zero, is $25,200.25. - **Education Coefficient (2905.35)**: This estimate suggests that each additional year of education is associated with an increase in income by $2,905.35. - **Pr(>|t|) Values and Significance Levels**: Both coefficients (Intercept and Education) are highly significant, as indicated by the very small p-values (3.08e-10 and 1.49e-12) which are less than 0.001, denoted by the triple asterisks (***). - **Residual Standard Error (32400)**: The average amount that a response will deviate from the true regression line. - **Multiple R-squared (0.7602)**: This value indicates that approximately 76.02% of the variability in annual income can be explained by the years of education. This regression model demonstrates a strong positive relationship between years of education and annual income among the surveyed Californians.
### Educational Exercise **Question:** What percentage of the variation of income is explained by education? Do not use decimal place, round and input whole integer percentage such as x or xx. So if answer is 58.3% then you would input 58. **Answer:** \[ \_\_\_\_\_\_\_\_\_\_ \] **Instructions:** - Analyze the given question properly. - Note that percentages should not have any decimal points. - Input the rounded whole number integer as your answer in the provided space.
Transcribed Image Text:### Educational Exercise **Question:** What percentage of the variation of income is explained by education? Do not use decimal place, round and input whole integer percentage such as x or xx. So if answer is 58.3% then you would input 58. **Answer:** \[ \_\_\_\_\_\_\_\_\_\_ \] **Instructions:** - Analyze the given question properly. - Note that percentages should not have any decimal points. - Input the rounded whole number integer as your answer in the provided space.
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