Compute the sample variance of age as well as the sample

Introductory Econometrics

Autumn Assignment

In an earlier tutorial, you were introduced to a data set that came from a job training experiment conducted for low-income men in the United States in 1976. In this question, you are given extra information for 5 individuals in the data set. The data is given as follows:

Observation

re78

educ

age

1

9.93

16

25

2

3.59

12

20

3

7.50

9

55

4

4.05

12

21

5

8.47

12

40

You will operate on the above data of 5 observations throughout this assignment. The variables are defined as follows:

re78 = earnings in 1978, measured in thousand dollars

educ = years of education

age = individual's age in years

(a) Reconstruct the following frequency table on your answer sheet and fill in the missing information.

 

Age<30

Age>=30

Educ<10

 

 

Educ>=10

 

 

(b) Reconstruct the following table on your answer sheet. Compute the conditional means.

 

Answer

E(re78|educ=12)

 

E(re78|educ<10)

 

E(re78|educ<10 and age<30)

 

E(re78|educ>=10 and age<30)

 

(c) Compute the sample variance of age, as well as the sample covariance between re78 and age.

(d) Use the OLS formula in lecture 2 to compute the sample regression line of the regression of re78 on age. (Note: round your answers to 3 significance figures)

(e) Suppose you regress re78 on age using observation 1 only. What result will you get? Briefly explain why this result occurs.

(f) Suppose the population model is

re78 = 1 + 0.1 x age + u.

On your answer sheet, reconstruct the following table and fill in the missing information.

Observation

re78 (Y)

age (X)

E(Y|X)

u

Predicted Y (Y^)

Residual ( u^)

1

9.93

25

3.5

6.43

6.10

3.83

2

3.59

20

 

 

 

 

3

7.50

55

 

 

 

 

4

4.05

21

 

 

 

 

5

8.47

40

 

 

 

 

(g) In part (f), the random errors are all larger than zero. Does it imply that the population model is incorrect? Briefly explain.

(h) This question continues part (d). The rest of the estimation result is:

re78 = β^1 + β^age x age

se: (3.310)

(0.095)

t-stat: (1.207)

(0.889)

p-val: (0.314)

(0.440)

Briefly interpret the coefficients (values given in part (d)) and the p-values in this regression.

(i) We are interested in testing the following hypothesis:

H0: bage = -0.1; H1: bage > -0.1

With the aid of a statistical table, find the critical value associated with a significance level of 10 percent. Is the null hypothesis rejected at the 10 percent significance level?

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