Question:
The data needed to answer this question are in Assignment3.dat, which is a subset of a larger dataset on wages and attributes of husband and wives in American households. The data are HW=husband's wage in 1975 dollars (sorry for the old data); HE=husband's education attainment in years; HA=husband's age in years; and CIT, which is a variable equal to 1 if the household lives in a large city and equal to zero otherwise. There are 753 observations in the dataset.
1. Estimate the model
HWt = β1 + β 2HEt + β3HAt + et
and include the regression output.
2. Perform a test of overall significance on model (1) using a level of significance of five percent. Make sure you interpret the outcome of your test. If R reports the numbers (test stat, p-value, etc.) you need to carry out the test, you can use them directly without having to show the calculations leading to these numbers.
3. Perform a RESET test on model (1) using a level of significance of five percent. Make sure you interpret the outcome of your test. Include any R regression output you need to carry out the test. If R reports the numbers (test stat, p-value, etc.) you need to carry out the test, you can use them directly without having to show the calculations leading to these numbers. Add a single power of the fitted values to run the test.
4. We now augment model (1) with explanatory variables HE^{2} and HA^{2}:
HWt = β1 + β 2HEt + β 3HAt + β 4HE^{2} t + β 5HA2t + et
Estimate this model, report the regression output, and use the regression output to argue whether HE^{2} and HA^{2} should or should not be part of the model
5. Perform a RESET test on model (2) using a level of significance of five percent. Make sure you interpret the outcome of your test. Is the outcome of the RESET test consistent with your answer to the previous question? Include any R regression output you need to carry out the test. If R reports the numbers (test stat, p-value, etc.) you need to carry out the test, you can use them directly without having to show the calculations leading to these numbers. Add a single power of the fitted values to run the test.
6. Using the estimated model from Question 4, calculate the change in predicted HW from a one year increase in HE (holding HA constant) for a husband with education attainment of 12 years. Answering this question requires the use of calculus.
7. Test whether a husband living in a large city has a higher wage than one living outside a large city (holding education attainment and age constant). Use a level of significance of five percent. Explain what you are doing. Include any R regression output you need to carry out the test. If R reports the numbers (test stat, p-value, etc.) you need to carry out the test, you can use them directly without having to show the calculations leading to these numbers. You have to make the call about which of models (1) or (2) you should choose.