Question 1 Name (Last First) _________________________________________ Email ID: email@example.com ECON 306 Homework 3 Due: Tuesday October 20 2015 Instructions: Please print out and complete the following assignment writing your answers clearly and showing your work directly on the assignment. Please keep a log of your work in STATA and print out and attach all of your results. Use a highlighter to highlight all of your commands in STATA (this will make it easier for the graders to see your work). Follow directions carefully (underlining or circling where indicated in your STATA output). Be sure to turn the assignment in at the beginning of class on Tuesday October 20. Late homeworks cannot be accepted. 2 1. (27 points total. 9 parts worth 3 points each.) With this assignment you will find a data file called HW3.Sleep. This data represents a part of a study that looked at the tradeoff between time spent sleeping and working as well as other factors that affect sleep. For reference the variables in this file are: sleep = min sleep at night per week totwrk = min worked per week educ = years of schooling age = in years Open this dataset within STATA. Before you begin answering the following it?s not a bad idea to ask STATA to summarize the data using the command summarize. As you complete this assignment be sure to save/store all of your STATA results. a. Run the following regression: (Label this Model 1 in your STATA output) ???????????????????? ? = ????0 + ????1 ? ???????????????????????? + ????2 ? ???????????????? + ????3 ? ???????????? b. At a level of ?=.05 for which if any values of ?i would you reject the null hypothesis that ?i=0? (If this applies write your answer in the space below AND circle in the STATA output) c. What percentage of the variation in sleep is explained by the three X-variables? (Write your answer below and underline in STATA output) 3 d. What is the predicted sleep with totwrk=2400 educ=16 age=28? e. According to this model how much will sleep change as age increases by 15 years? f. Test the hypothesis that the coefficients on educ and age are jointly significant at a level of ?=.05. Do this by (1) writing down the formula for the relevant F-statistic in the space below using the formula from class. Calculate it by running the appropriate restricted regression (this restricted version of the regression will be called Model 2.) (2) Indicate the critical F-value below and make a decision about the hypothesis. g. After calculating the F-statistic this way run the appropriate STATA command to confirm your answer (the ?short-cut? way discussed in class). Circle this in the STATA output. 4 h. Return to Model 1. Now perform a test of overall significance at a level of ?=.05. Do this by (1) writing down the formula for the relevant F-statistic in the space below using the formula from class. (2) Indicate the critical F-value and make a decision about the hypothesis. i. Confirm your results by indicating that the STATA output shows the same answer (circle in the STATA output). 5 2. (15 points total. 5 parts worth 3 points each.) Suppose you are running a model to look at the determinants of earnings. After running your data in STATA you get the following output: Several of the numbers in the STATA output have been intentionally covered up. a) Solve for the standard error of the coefficient for height (Show your work): b) Solve for the t-statistic for education (Show your work): c) Solve for the coefficient for age (Show your work): d) Interpret the F-statistic and corresponding p-value STATA has calculated. What does this tell us? _cons -49740.73 3289.248 -15.12 0.000 -56187.97 -43293.48 age 333.2802 18.32877 18.18 0.000 297.3541 369.2064 educ 3945.646 70.03849 56.34 0.000 3808.364 4082.929 height 441.5084 46.61546 9.47 0.000 350.1376 532.8792 earnings Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 1.2953e+13 17869 724863544 Root MSE = 24538 Adj R-squared = 0.1693 Residual 1.0758e+13 17866 602125581 R-squared = 0.1695 Model 2.1950e+12 3 7.3167e+11 Prob > F = 0.0000 F( 3 17866) = 1215.15 Source SS df MS Number of obs = 17870 . regress earnings height educ age 6 Consider a model where we regress Earnings on Height only: d) What is the value of the t-statistic for height? Explain how you know this. _cons -512.7336 3386.856 -0.15 0.880 -7151.299 6125.832 height 707.6716 50.48922 14.02 0.000 608.7078 806.6353 earnings Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 1.2953e+13 17869 724863544 Root MSE = 26777 Adj R-squared = 0.0108 Residual 1.2812e+13 17868 717020563 R-squared = 0.0109 Model 1.4086e+11 1 1.4086e+11 Prob > F = 0.0000 F( 1 17868) = 196.46 Source SS df MS Number of obs = 17870 . regress earnings height
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