Consider the following model (): where y is the annual income; x is the number o
ID: 3358017 • Letter: C
Question
Consider the following model (): where y is the annual income; x is the number of years of work experience H is a dummy variable =1 if a person has a Harvard degree, P is a dummy variable 1 if a person has a Princeton degree. The reference group is Auburn graduates. (a) How would you interpret the coefficients in the above model? (b) In detail, explain how would you test the following hypotheses: (0 H082-0 and (ii) H0:2=A3? (Assume a two-sided alternative.) Now consider the model (II): (c) What is the difference between models () and (I)? (d) Interpret the coefficients of this model. 2 (e) How would you test the hypothesis that 4 = 5? If you fail to reject this hypothesis, what would that imply about the model?Explanation / Answer
Answer A :
0 is the value of average annual income irrespective of numbers of years of experience and attended college.
1 is the value of change in annual income for one unit change in years of experience.
2 is the measure of the differene in mean annual income resulting from changing from Princeton degree to other degree.
3 is the measure of the differene in mean annual income resulting from changing from Harvard degree to other degree.
Answerb :
testing of 2=0 would be done by t-test using t statistic as t=(2)/SE(2) ~ t (/2,n-2)
testing of 2=3 would be done by t test using t statistic as t=2-3/ Sqrt (MSres/Sxx)
Answer C :
The model II involves interaction between dummy variable and continuous variable i.e. the years of experience and college degree.
Answer d :
The interpretation for 0, 1,2 and 3 remains same as in model I. 4 is the measure of the differene in mean annual income resulting from changing from years of experience with Harvard degree to years of experience with other degree.
5 is the measure of the differene in mean annual income resulting from changing from years of experience with Princeton degree to years of experience with other degree.
Answer e : The hypothesis 4 =5 can be testing usinf F test. If hypothesis is accepted, we would infer that ther is no significance difference in mean annual income of an experienced person having degree from Harvard and an experienced person having degree from Princeton.