a. What is the regression equation? Please write it out, including the residual term. b. What is the equation we use to predict educational attainment with mother's educational attainment? In other words, what do we have to do with the equation in (a) in order to make predictions? c. What is a person's predicted years of schooling completed when their mother has a 10h grade education? d. What is a person's predicted years of schooling completed when their mother has a high school diploma? e. What is a person's predicted years of schooling completed when their mother has a four-year baccalaureate degree? f. What is a person's predicted years of schooling completed when their mother has completed a two-year graduate degree on top of their four-year baccalaureate degree? Coefficients: Estimate Std. Error t value Pr(>|t|) <2e-16 *** (Intercept) 9.85795 maeduc 0.18121 54.40 0.34519 0.01475 23.41 <2e-16 *** --- Signif. codes: 0 **** 0.001 '**' 0.0i *'0.05 '.' 0.1 ' ' 1 Residual standard error: 2.734 on 2269 degrees of freedom (267 observations deleted due to missingness) Multiple R-squared: 0.1945, Adjusted R-squared: F-statistic: 547.9 on 1 and 2269 DF, p-value: < 2.2e-16 0.1942
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Assuming,
Let y = Dependent variable = years of schooling completed by Respondent,
Let x = Independent variable = years of schooling completed by Respondent's mother.
Now, Using the values provide in the Table given in the Question :
(a) The regression equation is:
Regression equation: y = a + bx + ɛ
y is the value of the dependent variable (y), what is being predicted or explained.
a, a constant, equals the value of y when the value of x = 0.
b is the coefficient of X, the slope of the regression line, how much Y changes for each change in x.
x is the value of the independent variable (x), what is predicting or explaining the value of y.
ɛ is the error term, the error in predicting the value of y, given the value of x
There equation is : Y = 9.85795 + 0.34519 x + e (Here, e is residual term).
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