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As a person increases their years of education by 1 unit (1 year), how much do we estimate their expected income to increase? Round to the nearest 2nd decimal place, x.xx

As a person increases their years of education by 1 unit (1 year), how much do we estimate their expected income to increase? Round to the nearest 2nd decimal place, x.xx

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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**Educational Resource: Estimating Income Increase with Additional Education** --- **Question:** As a person increases their years of education by 1 unit (1 year), how much do we estimate their expected income to increase? Round to the nearest 2nd decimal place, x.xx [Input Box for the Answer] --- **Explanation:** This question investigates the relationship between education and expected income. Typically, studies show that additional years of education can positively impact income levels. This exercise helps understand how to quantify this relationship, likely in the context of a statistical or economic analysis course. --- Please provide your answer in the text box provided.
Transcribed Image Text:**Educational Resource: Estimating Income Increase with Additional Education** --- **Question:** As a person increases their years of education by 1 unit (1 year), how much do we estimate their expected income to increase? Round to the nearest 2nd decimal place, x.xx [Input Box for the Answer] --- **Explanation:** This question investigates the relationship between education and expected income. Typically, studies show that additional years of education can positively impact income levels. This exercise helps understand how to quantify this relationship, likely in the context of a statistical or economic analysis course. --- Please provide your answer in the text box provided.
### Relationship Between Education and Annual Income A survey is conducted on 700 Californians older than 30 years of age. The study aims to obtain inferences on 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. To explore this relationship, a simple linear regression model is fit to the data, and the output from the statistical software R is displayed 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 *** ``` ### Interpretation of the Results 1. **Intercept**: - **Estimate**: 25200.25 - **Interpretation**: The average annual income for someone with 0 years of education is $25,200.25. - **Standard Error**: 1488.94 - **t value**: 16.93 - **Pr(>|t|)**: 3.08e-10 (highly significant, indicated by `***`) 2. **Education**: - **Estimate**: 2905.35 - **Interpretation**: For each additional year of education, the average annual income increases by $2,905.35. - **Standard Error**: 112.61 - **t value**: 25.80 - **Pr(>|t|)**: 1.49e-12 (highly significant, indicated by `***`) ### Additional Statistics - **Residual standard error**: 32400 (on 698 degrees of freedom) - This value is an estimate of the standard deviation of the residuals (the differences between observed and predicted values). - **Multiple R-squared**: 0.7602 - This indicates that approximately 76.02% of the variability in annual income can be explained by the years of education. ### Conclusion The linear regression analysis suggests a significant positive relationship between years of education and annual income among Californians over 30 years of age.
Transcribed Image Text:### Relationship Between Education and Annual Income A survey is conducted on 700 Californians older than 30 years of age. The study aims to obtain inferences on 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. To explore this relationship, a simple linear regression model is fit to the data, and the output from the statistical software R is displayed 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 *** ``` ### Interpretation of the Results 1. **Intercept**: - **Estimate**: 25200.25 - **Interpretation**: The average annual income for someone with 0 years of education is $25,200.25. - **Standard Error**: 1488.94 - **t value**: 16.93 - **Pr(>|t|)**: 3.08e-10 (highly significant, indicated by `***`) 2. **Education**: - **Estimate**: 2905.35 - **Interpretation**: For each additional year of education, the average annual income increases by $2,905.35. - **Standard Error**: 112.61 - **t value**: 25.80 - **Pr(>|t|)**: 1.49e-12 (highly significant, indicated by `***`) ### Additional Statistics - **Residual standard error**: 32400 (on 698 degrees of freedom) - This value is an estimate of the standard deviation of the residuals (the differences between observed and predicted values). - **Multiple R-squared**: 0.7602 - This indicates that approximately 76.02% of the variability in annual income can be explained by the years of education. ### Conclusion The linear regression analysis suggests a significant positive relationship between years of education and annual income among Californians over 30 years of age.
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