**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 IncomeA 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:```Rlm(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 Results1. **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.### ConclusionThe linear regression analysis suggests a significant positive relationship between years of education and annual income among Californians over 30 years of age.

From the given output, the coefficient for education is 2905.35.The slope of the regression line…

Answered: As a person increases their years of…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 14CR

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