Data on working men was used to estimate the following equation: educ= 10.36 - .
ID: 2440092 • Letter: D
Question
Data on working men was used to estimate the following equation:
educ= 10.36 - .094sibs + .131meduc + .210feduc
Where educ is years of schooling, sibs is the number of siblings, meduc is mother’s years of schooling, and feduc is father’s years of schooling. Here n = 722, R2 = .214.
A) Does sibs have the expected effect? Explain.
B) Holding meduc and feduc fixed, by how much does sibs have to increase to reduce predicted years of education by one year? (Hint: The answer is a non-integer.)
C) Suppose the standard error on sibs is found to be .012. Is sibs statistically significant? Explain. (You don’t need to formally test the hypothesis, though you may wish to do so in order to check your answer.)
Explanation / Answer
A) Yes Sibs has expected effect. Higher the number of siblings in the family, lower is the number of years of schooling a man can have. This is so because parents have to spend more if they have more than one child.
B) change in educ = - 0.094* change in sibs
Change in educ is -1
Change in sibs = -1/(-0.094) = 10.64
Sibs has to increase by 10.64.
C) z= B / SE
B is the slope coefficient, here it is 0.094
SE is standard error, here it is 0.012
z= 0.094/0.012 = 7.83
calculated z statistics is lower than critical z statistics of 1.96 at 5% level of significance.
Therefore we reject the null hypothesis and conclude that sibs is statistically significant.
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