This question is a Ph.D. level question, and it has all the needed information.

Question

This question is a Ph.D. level question, and it has all the needed information. Please answer with details, many thanks!

8. Consider the following regression with respect to female labor participation (y) on years of education (z): yi 3a Bari ui, i 1,2, ...,n where y is binary (0 or 1, 1 signifying the woman chooses to work) and is measured in years 0). Assume that after OLS, we obtain the parameters of the model as 0.146 +0.038zi ui (0.121) (0.014) where the number below the estimated coefficient in parantheses is the standard error of the estimate. With the above information, answer the following: (a) Interpret the estimated coefficient for a. Does this seem reasonable? (b) Interpret the estimated coefficient for B. Does this seem reasonable? (c) Test the null that the coefficient in part (a) is zero. Test the null that the coefficient in part (b) is zero. (d) Draw a figure with probability of labor force participation on the vertical axis and years of education on the horizontal axis. Draw and label the regression line. (e) How many years of education does it take before labor force participation is possible (positive probability How many years of education does it take for labor force participation to be immi nent?

Explanation / Answer

Here dependent variable y = female labor participation and

independent variable x = years of education

a and b part :

Given that the regression equation is,

yi = -0.146 + 0.038xi + ui

(0.121) (0.014)

Here intercept = -0.146 and

slope = 0.038

Interpretation of intercept and slope :

If we take years of education as 0 then we get female labor participation is -0.146 unit.

One unit change in years of education will be 0.038 unit increase in female labor participation.

c) Here we have to test two hypothesis that,

H0 : a = 0 Vs H1 : a not= 0

H0 : B = 0 Vs H1 : B not= 0

Assume that, alpha = level of significance = 5% = 0.05

Here test statistic follows t-distribution with n-2 degrees of freedom.

The test statistic is,

t = b / SEb

where b is sample slope for data.

SEb is standard error of the estimate

t = -0.146/0.121 = -1.21

t = 0.038/0.014 = 2.71

Now we have to find P-value for taking decision.

P-value we can find by using EXCEL.

syntax :

=TDIST(x, deg_freedom, tails)

where x is absolute value of test statistic.

deg_freedom = n-2

Here n is not mentioned.

For example if we take n is 30 then

deg_freedom = 30-2 = 28

tails = 2

P-value (intercept) = 0.2364

P-value (slope) = 0.0112

We see that P-value (intercept) > alpha

Fail to reject H0 at 5% level of significance.

Conclusion : The population intercept may be 0.

P-value (slope) < alpha

Reject H0 at 5% level if significance.

COnclusion : The population slope for years of education is differ than 0.

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