20 points. (Adapted from Erankfort-Nachmias & Leon-Guerrero 2006) Social scienti
ID: 3367124 • Letter: 2
Question
20 points. (Adapted from Erankfort-Nachmias & Leon-Guerrero 2006) Social scientists have long been interested in the aspirations and achievements eople in the United States. Is there an association between the education level of mothers and their children? The General Social Survey includes questions to collec information on the educational level of respondents and their mothers. Consider the following 2002 GSS data, which you can consider a random sub-sample: Mother's Education in Respondent's Education Years in Years 12 18 15 10 18 12 14 12 10 12 15 16 16 14 18 15 14 18 12 RSS 20.83 Draw a scatterplot of these data. Put the independent variable on the X-axis and the dependent variable on the y-axis. What is the equation for the regression (prediction) line for this data? Interpret the meaning of the regression coefficients a and b What is the predicted value for respondent's education when mother's education is equal to 16? 722 Compoute R2 and interpret its meaningExplanation / Answer
me <- c(9,12,18,15,10,18,12,14,12,10);me
re<- c(12,15,16,16,14,18,15,14,18,12);re
df <- data.frame(me,re);df
regressor <- lm(re ~ me ,data= df )
summary(regressor)
Call:
lm(formula = re ~ me, data = df)
Residuals:
Min 1Q Median 3Q Max
-1.6304 -1.2554 0.2283 0.4565 3.4565
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.0652 2.2455 4.037 0.00375 **
me 0.4565 0.1682 2.714 0.02650 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.613 on 8 degrees of freedom
Multiple R-squared: 0.4793, Adjusted R-squared: 0.4143
F-statistic: 7.365 on 1 and 8 DF, p-value: 0.0265
respondent's education is 16.49.
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