1. Data on the weekly sales of a major brand of canned tuna by a supermarket chain in a large mid-western US city during a mid-1990's calendar year are contained in the file tuna. dta. The file contains 52 observations on the following variables sal1 = unit sales of brand no.1 of canned tuna, apr1 = price per can of brand no.1 of canned tuna, apr2, apr3 = price per can of brands nos. 2 and 3 of canned tuna, disp = 1 if there is a store display for brand 1 but no newspaper ad, 0 otherwise dispad = 1 if there is a store display and a newspaper ad for brand 1, 0 otherwise We estimated the log-linear model: log(sall) = 81 + 8zapr1 + 83apr2 + Bapr3 + 8sdisp + Sodispad +e and obtained the following Stata outcome; gen log_sall = logisall) . regress log_sall aprl apr2 apr3 disp dispad source 55 of Number of obs = 52 F1 5. 401 3 49.33 Model 28 . 4564198 5 5.69128397 Prob > F 0. 0000 Residual 5.30725263 46 . 115375057 R-squared 0. 8428 Adj R-squared 8. 8257 Total 33. 7636725 51 . 662032793 Root MSE . 33967 log_sall Coef. Std. Err. t [95% Conf. Interval] aprl -3. 746301 5765177 -6.50 0.080 -4.906771 -2. 585831 pr2 1. 149494 - 4486429 2.56 6. 014 246423 2. 052566 spry 1. 288049 6053247 2 . 13 0.039 0695934 2. 506504 disp 4237441 1052095 1.03 2119085 6355198 dispad 1. 431253 . 1561625 9.17 1. 116914 1. 745592 _cons 0. 904812 - 6463663 10.90 9.080 7. 683744 10.20586(a) In order to see if this model has omitted variables, we ran the following command, estat ovtest and obtain the p value of 0.057. State precisely the null hypothesis associated with this test (5 marks) and decide whether to reject the null hypothesis using your own level of the test (5 marks).(b) Discuss and interpret the estimates of 83. Especially, show, step-by-step, that the marginal effect is given as Osal1 dapr2 = Basa12 (5 marks). Then, explain the effect of a one-unit increase in the price of Brand 2 on sales using the Stata outcome. (5 marks).(c) What is the estimated percentage increase in sales from a display and no adver- tisement? (5 marks)2. Mroz (1987, Econometrica, 55:765-800) investigated the labour force participation of married women. Consider the model hours = 81 + 82 log(wage) + 8seduc + Bage + 8skids16+ Skids618+ Synwiffincte where the errors are assumed to be independent NV(0,o') random variables. The variable nwiffinc = faminc - wage x hours. The variable Ifp is a binary variable that takes the value 1 if a woman worked and 0 if she did not. The variable exper is the years of experience. (a) Explain why log(wage) can be endogenous. (5 marks)(b) Explain why exper and exper- can be valid instruments to correct the endo- geneity problem in (a). (5 marks)(c) After estimating the regression equations by the 2SLS with exper and exper- as instrument variables, we performed the Stata command and obtained the results as shown below. Interpret First-state regression summary statistics: es- pecially, what can you say about the instrumental variables? (5 marks)estat firststage First-stage regression summary statistics Adjusted Partial Variable R-5q. R-SQ. R-5q. F (2, 420) Prob > F Log_wage 0. 1641 0. 1502 0. 0378 8. 25024 0.0003 Minimum eigenvalue statistic = 8.25024 Critical Values * of endogenous regressors: N H Ho: Instruments are weak # of excluded instruments: 5% 10% 20% 304 25LS relative bias (not available) 10% 15% 20% 25% 2545 Size of nominal 5% Wald test 19.93 11.59 8 . 75 7.25 LIML Size of nominal 5% Wald test 8.68 5.33 4.42 3.92 (d) The following computer log and output are related to a hypothesis testing to see whether log(wage) is endogenous using exper and exper- as instrumental variables. Precisely state the null hypothesis (5 marks), explain the test proce- dure step-by-step and make a conclusion about the endogeneity using the Stata outputs