1. You examine how a teacher's experience (variable exp, measured in years) affects his or her wage (variable salary, measured in thousands of dollars) using the linear regression below: reg salary exp Source SS df MS Number of obs = 3921 F( 1, 3919) = 3912.27 Model 577731. 231 1 577731.231 Prob > F = 0 . 0000 Residual 578725 . 039 3919 147 . 67161 R-squared 0. 4996 Adj R-squared = 0. 4994 Total 1156456. 27 3920 295.014355 Root MSE = 12 . 152 salary Coef. Std. Err. t P>It| [95% Conf. Interval] exp 2. 793023 . 044654 62.55 0. 000 2. 705475 2. 88057 cons 58 . 46001 . 3859321 151 . 48 0. 000 57 . 70336 59 . 21665 (a) (4 points) Write down the prediction equation of this regression. (b) (6 points) Interpret the coefficients of this regression. (c) (6 points) Test that a one-year increase in a teacher's experience increases his or her wage by more than 2.7 thousand dollars per year, using a 5% significance level.2. You are interested in seeing how a variety of factors affect the happiness of a country's citizens. You download the 2017 World Happiness Index from the United Nations and run the following regression of happiness on freedom score (freedom), trust of government score (trustgov), and GDP per capita (gapcapita). reg happinessscore freedom trustgov gapcapita Source SS df MS Number of obs 155 F (3, 151) 147 . 41 Model 146. 908804 3 48.9696015 Prob > F D. 0000 Residual 50. 1621491 151 . 332199663 R-squared 0 . 7455 Adj R-squared 0. 7404 Total 197 . 070954 154 1.27968152 Root MSE 57637 happinesss~e Coef. Std. Err. t P>ItI [954 Conf. Interval] freedom 2.227434 . 3680995 6. 05 0.000 1 . 500144 2. 954725 trustgov 4422988 . 5388779 gapcapita 1. 853005 1214193 15. 26 0.000 1. 613105 2. 092905 cons 2.564332 . 1519676 16.87 0.000 2. 264074 2. 864589 (a) (3 points) The United States has a GDP per capita of 1.546, a freedom score of 0.5057, and a trust in government score of 0.1356. What is the predicted happiness score for the United States? (b) (6 points) Test that the partial slope coefficient on trust gov is zero at the 1% significance level. Show your steps. Interpret your conclusion. (c) (6 points) Is a one unit increase in the freedom score associated with a larger than 2 points increase in the happiness index? Show all steps. Use 5% significance level. (d) (2 points) Interpret the confidence interval for gapcapita. (e) (5 points) Calculate an interpret a 99% confidence interval for the coefficient on freedom