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Say we have two people, where person 1 has 5 years more education than person 2. How much more income do we estimate person 1 to make compared to person 2? Round to the nearest 2nd decimal place, x.xx

Say we have two people, where person 1 has 5 years more education than person 2. How much more income do we estimate person 1 to make compared to person 2? Round to the nearest 2nd decimal place, x.xx

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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**Description:** **Question:** Say we have two people, where person 1 has 5 years more education than person 2. How much more income do we estimate person 1 to make compared to person 2? Round to the nearest 2nd decimal place, x.xx.
Transcribed Image Text:**Description:** **Question:** Say we have two people, where person 1 has 5 years more education than person 2. How much more income do we estimate person 1 to make compared to person 2? Round to the nearest 2nd decimal place, x.xx.
### Relationship Between Years of Education and Yearly Income: A Study on Californians **Overview:** A survey was conducted on 700 individuals in California, each over 30 years of age. The objective of the study was to infer the relationship between the number of years of education and yearly income in dollars. Here, the income in dollars is the response variable, while the number of years of education serves as the explanatory variable. **Methodology:** A simple linear regression model was utilized to analyze the data. The output obtained from R for the linear regression is presented below: **R Output:** ``` 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 Statistics:** - Residual standard error: 32400 on 698 degrees of freedom - Multiple R-squared: 0.7602 **Interpretation:** 1. **Intercept (25200.25):** This coefficient represents the estimated average income for individuals with zero years of education. While it may not have a practical interpretation in this context, it serves as the baseline for the model. 2. **Education (2905.35):** This coefficient indicates that for each additional year of education, the yearly income increases by an estimated $2905.35, holding other factors constant. This suggests a positive relationship between education and income. 3. **Residual Standard Error (32400):** This value measures the typical deviation of observed income values from the regression line. A lower value would indicate a better fit of the model to the data. 4. **Multiple R-squared (0.7602):** This statistic indicates that approximately 76.02% of the variability in income can be explained by the number of years of education. A higher R-squared indicates a stronger relationship between education and income. 5. **Significance Levels:** - The `Pr(>|t|)` value for both coefficients is very low (close to zero), and the presence
Transcribed Image Text:### Relationship Between Years of Education and Yearly Income: A Study on Californians **Overview:** A survey was conducted on 700 individuals in California, each over 30 years of age. The objective of the study was to infer the relationship between the number of years of education and yearly income in dollars. Here, the income in dollars is the response variable, while the number of years of education serves as the explanatory variable. **Methodology:** A simple linear regression model was utilized to analyze the data. The output obtained from R for the linear regression is presented below: **R Output:** ``` 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 Statistics:** - Residual standard error: 32400 on 698 degrees of freedom - Multiple R-squared: 0.7602 **Interpretation:** 1. **Intercept (25200.25):** This coefficient represents the estimated average income for individuals with zero years of education. While it may not have a practical interpretation in this context, it serves as the baseline for the model. 2. **Education (2905.35):** This coefficient indicates that for each additional year of education, the yearly income increases by an estimated $2905.35, holding other factors constant. This suggests a positive relationship between education and income. 3. **Residual Standard Error (32400):** This value measures the typical deviation of observed income values from the regression line. A lower value would indicate a better fit of the model to the data. 4. **Multiple R-squared (0.7602):** This statistic indicates that approximately 76.02% of the variability in income can be explained by the number of years of education. A higher R-squared indicates a stronger relationship between education and income. 5. **Significance Levels:** - The `Pr(>|t|)` value for both coefficients is very low (close to zero), and the presence
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