### Analysis of the Relationship Between Education and IncomeA survey was conducted on 700 Californians older than 30 years of age. The study aims to derive inferences about the relationship between years of education and yearly income in dollars. Here, the response variable is the income in dollars, and the explanatory variable is the number of years of education.A simple linear regression model was applied, and the results obtained from R are presented below:#### Linear Model```Rlm(formula = Income ~ Education, data = CA)```### Coefficients:| 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 *** |**Residual standard error**: 32400 on 698 degrees of freedom **Multiple R-squared**: 0.7602 ### Explanation:1. **Intercept (Estimate = 25200.25)**: - This is the estimated average income (in dollars) when the number of years of education is zero. The high t-value (16.93) and the very small p-value (3.08e-10) indicate that this estimate is significantly different from zero.2. **Education (Estimate = 2905.35)**: - This represents the estimated increase in income (in dollars) for each additional year of education. The high t-value (25.80) and the very small p-value (1.49e-12) indicate that this coefficient is also significantly different from zero.3. **Residual Standard Error (32400)**: - This statistic measures the average amount that the observed values deviate from the predicted values. 4. **Multiple R-squared (0.7602)**: - This value indicates that approximately 76.02% of the variation in the income can be explained by the number of years of education.The presence of the three stars (***) next to the p-values in the coefficient table indicate a high level of statistical significance.This analysis suggests that there is a strong, positive relationship between years of education and yearly ### Writing the Estimated Linear Equation#### Instructions:Write out the estimated linear equation. Round to two decimal places (x.xx).\[ \hat{Income_i} = \quad \_\_\_\_\_\_ \quad + \quad \_\_\_\_\_\_ \quad \text{Education}_i \]*Note:* The equation is in the form of a linear regression equation where $\hat{Income_i}$ is the estimated income based on the level of education ($\text{Education}_i$). The coefficients to be determined are the intercept and the slope for the variable Education.

The information provided in the question are as follows :-Number of Californians surveyed = 700The…

Answered: A survey is conducted on 700…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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Consider a regression model. The coefficient of determination (R2) gives the proportion of the variability in the dependent variable that is explained by the regression equation. True False
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