Problem 4: (10 points) Consider the stochastic processes given below, where &, is normally distribu- ted white noise. For each process determine whether it is covariance station nary, strictly covariance stationary, or integrated of order one fie. / (1)], or neither of these: 1. X = 1+t+ 2. (1 - 1, 14 + 0, 1823 ) X = 3. X1 = 1-1Problem 3: (10 points) Humans are analyzed regarding their weight and height. The STATA output shows the results of regressing weight (WEIGHT85, measured in pounds) on height (HEIGHT, measured in inches), first with a linear specification and then with a logarithmic one (LNWEIGHT85=log(WEIGHT85), LN- HEIGHT=log(HEIGHT)), including a dummy variable MALE (MALE= 1 if the observation unit is a man, otherwise () in both cases. Interpret all regression coefficients of both regressions. 1. reg WEIGHT85 HEIGHT MALE Source SS df MS Model 288595.144 2 44297.572 Residual 342677.256 537 638.132692 Total 631272.4 539 1171.19184 Number of obs = 540 F(2, 537) = 226.12 Prob > F = 0.0000 R-squared = 0.4572 Adj R-squared = 0.4551 Root MSE = 25.261 WEIGHT85 Coef. Std. Err. t P > t 95% Conf. Interval HEIGHT 4.155447 .3950937 10.52 0.000 3.379328 4.931565 MALE 15.52953 3.197231 4.86 0.000 9.24892 21.81015 cons -133.8471 25.51672 -5.25 0.000 -183.9719 -83.72223 2. reg LNWEIGHT85 LNHEIGHT MALE Source SS df MS Model 12.3281409 2 6.16407045 Residual 12.5598134 537 023388852 Total 24.8879543 539 .046174312 Number of obs = 540 F(2, 537) = 263.55 Prob > F = 0.0000 R-squared = 0.4953 Adj R-squared = 0.4935 Root MSE = .15293 LNWEIGHT85 Coef Std. Err. P > t [95% Conf. Interval LNHEIGHT 1.760394 1611105 10.93 0.000 1.44391 2.076878 MALE 1 108935 0193434 5.73 0.000 .0728955 1488914 cons -2.451119 6711458 -3.65 0.000 -3.769512 -1.132726Problem 1: [2!] points} A health economist plans to evaluate whether screening patients on arrival or spending extra moneyr on cleaning is more e'ective in reducing the inci- dence of infections by the MESA bacterium in hospitals. She hypothesizes the following model: MHSAi 2 $1 + Liz-5i + Sac; + m. where. in hospital 1'. MESA is the number of infections per thousand patients1 S is expenditure per patient on screening, and C is expenditure per patient on cleaning. u; is a disturbance term that satises the usual regression model assumptions. In particular. a; is drawn from a distribution with mean zero and constant variance o\". The researcher would like to t the relationship using a sample of hospitals. Unfortunately. data for individual hospitals are not available. Instead she has to use regional data to t m: - 1+i3231+ucj+ where m1,31.01.1 are the averages of MRSA.C. S. u Iior the hospitals in region 3'. There were different numbers of hospitals in the regions. there being of hospitals in region. 3'. 1. Show that the variance of 11.1 is equal to E and that a regression using ordinary least square! [0L5] to t the second equation will be subject to heteroseedaaticity. '2. Assmning that the researcher knows the value of n; for each region1 ex- plain how she could re-speeil'v the regression model to malre it homosce- dastic. State the revised specication and demonstrate mathematically that it is homosoedastic. ll. Suppose that the researcher did not know the values of n}. Explain in general terms [not mathematically} how, nevertheless. she could per- form I! teats relating to the regression coefcients. stating an}.r limitati- ons