. Solve the following attachments.

You are the lead biologist working on the ecology of an endangered squirrel (Squirrelus rockyji) in the Sierra Nevada above Porterville. You and colleagues have found a population in protected habitat. This habitat has recently been purchased for the squirrel and human disturbances have been eliminated. You have collected data on survival rates and fecundity for the population (Table 1). Table 1. Number of individuals (no), survival rate (s,), and fecundity (b.), by age at the start of the study. Age (x) Number (no) Survival Rate (S,) Fecundity (b.) 15 0.42 0.58 0.74 WN - 0.75 WARON- 0.74 0.75 0.25 0.15 0.0 a) What is the total population size at the start of the study? b) Project population numbers over the next nine years (10 years total) assuming a stable age distribution (see entries in Table 12.2, page 286 in your textbook for an example). Round numbers of adults surviving each year to whole numbers (e.g., 6.50 = 7, 3.49 = 3) before determining reproductive output for a year. c) Construct a table of numbers of individuals by age by time interval (year 0 to year 9). Also show N and A for each year (pattern table after Table 12.4 in text). Round N and A to two decimal places. d) Graph N against year (starting at year 0) and A against year. e) Finally, construct a Life Table (see Table 12.7) for this endangered squirrel showing x, Sx, bx, I., labx, and xl.b. values (list last three parameters to four decimal places). Calculate Ro, T, and ra for this population (to two decimal places). "NOTE: always use calculator values (out to 8 or 9 decimal places) when working equations even if you only report values to 2, 3, or 4 decimal places. Turn in: 1. Table of numbers of individuals by age by time interval. 2. Graph of N versus Year. 3. Graph of A versus Year. 4. Life Table, along with R., T, and r.. All tables and figures require captions.STAT 443: Time Series and Forecasting Lab 4: SARIMA Processes We have seen both autoregressive (AR) and moving average (MA) models, as well as hybrids of these known as autoregressive moving average (ARMA) models. While these are quite versatile models, recall that they are used to model series that are stationary. 1. Without using any mathematical notation, describe in words what it means for a time series to be stationary. 2. Consider a realization of a process given by the values (3.89, 8.04, 10.26, 10.72, 10.69, 12.50, 16.43, 20.15, 22.38, 22.45, 21.91, 24.06, 28.03, 32.35, 34.47, 34.47, 34.98, 36.36, 39.86, 43.57}. Enter these data into R, plot as a time series, and comment on whether the series appears to satisfy the requirements of stationarity. 3. One common way of removing a trend is to difference the data, where instead of looking at the time series {z, } we look at { } with MI = VI =I - -1. (Note this series will have one less term than the original.) Using the data above, determine and plot the differenced time series {yr}- Comment on the resulting plot and the act of {y ). A useful function here is diff (x, lag=1, difference=1), which returns suitably lagged and iterated differences. Use R help to learn about options lag and differences. 4. In order to remove a seasonal effect, we could difference over the seasonal period. For instance, take our de-trended data {y} and difference again but at a lag equal to the seasonal period, s. The new series will be where s is the period of the seasonal effect. Note the series will again become shorter, this time with s fewer terms. Choosing the appropriate value of s here, apply seasonal differenceng to the series from part 3 and plot the resulting series. Plot the act of Vayt- Does your V.M resemble white noise? 5. Suggest which type of model from the SARIMA family you would use for the original data. 6. Use the arima function to fit a SARIMA model to the original (undifferenced) time series Provide the estimates of any parameters.1. For which violation of the classical linear regression assumption does Durbin-Watson test is used for detection? And outline the procedure for the test merely formulating the hypotheses and stating the decision rule using the measure of autocorrelation, p, and the Durbin-Watson statistics, d-statistics. 2. The economic theory of investment states that investment expenditure at a given point in time (I) is negatively affected by interest rate at a given point in time (r). Suppose that the functional relationship in the stated economic theory is linear and estimated values of the intercept and slope are 82 and 0.6 respectively. Based on the stated economic theory and the associated information, derive the estimated econometric model and predicate the value of the dependent variable provided that 50 is given as value of the independent variable. 3. The following estimated equation was obtained by OLS regression using quarterly data for 1978 to 1996 inclusive. Y, = 2.20+0.104X, (3.4) (0.005) Standard errors are in parentheses, the explained sum of squares and the residual sum of squares were 109.6 and 18.48 respectively. Thus, a) Test a 5% level of significance for the statistical significance of the parameter estimates using t-test technique b) Test the overall test of significance ant 1% c) Calculate the coefficient of determination 4. Consider the following estimated regression model of monthly earnings of 25 employees selected at random from the pool of employees in a given organization. Assuming the monthly earning (ME) is affected by two explanatory variables-SEX and AGE of employees, the regression output is given as ME = -1.65+ 0.33SEX +0.4 AGE (-0.60) (0.18) (0.03) R' = 0.825 Given the standard errors of each estimate in brackets answer the following questions A. Test the statistical significance of the intercept using standard error test B. Test the statistical significance of SEX at 5% level of significance C. Test the overall significance of the model at 1% level of significance D. Interpret R21. A bit of practice with dummy variables and heferoskedasficify: Consider the following model for the logarithm of wage given years of university education and gender of person 1' : log(wage;) = g + oqfenmle, + lronmi; + lfemale; x 10mm,- + u; # where log is the natural logarithm, femlei is a dummy variable that is equal to 1 if person i is female is 0 otherwise, and 10mm",- is the number of years of university education that person 1' has. Based on a random sample of 6763 individuals, we have estimated this model using OLS and obtained the following estimated equation: _--_-__-_ log(wage,z) =3.289 0.360fenmle; +0. 050 forum,- +0.0309maie, x forum}, (0011) (0.015) (0.003) (0.005) 1':l,2,...,67l63,1l22 = 0.202. a. Explain how you would test the hypothesis that the conditional expectation of log(wage) conditional on years of university education is exactly the same for men and women. You need to specify the null and the alternative, the test statistic and its distribution under the null, the regression that you should run so that you can compute the test statistic, and the rule for rejection or non-rejection of the null hypothesis. c. Using the estimated equation, nd the value of tomni (total number of years in university) such that the predicted values of log(wage) are the same for men and women. Can women realistically get enough years of university education so that their earnings catch up to those of men? Explain. d. Suppose we suspect that the variation of Iog(wage) around its conditional mean is larger for women than it is for men. That means that in the