7) Suggest an appropriate specification of ARMA model for the data, for which the following results were provided to you by Matlab. Justify your choice - explain it. Write the general form of the ARMA model with the values (orders of the AR and MA part) that you have suggested. Sample Autocorrelation 1 0.8 0.6 0.4 0.2 0 -0.2 -04 0 2 4 Sample Autocorrelation Function 6 8 10 Lag 12 14 16 18 20 Sample Partial Autocorrelations 3.4214 2.9690 2.8886 2.8939 3.0126 2.9112 2.8948 2.8977 2.8597 2.8627 2.8694 2.8762 2.8527 2.8695 2.8731 2.8800 0.8 0.6 0.4 0.2 0 -0.2 -0.4 0 Sample Partial Autocorrelation Function 5 10 Lag 15 20 d the BIC matrix (BIC values for models of orders (0,0) to (3,3)) is the following one: BIC = 1.0e+03 *
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- An urban community wants to show that the incidence of breast cancer is higher in their locality than in a neighboring rural area. (PCB levels were found to be higher in the soil of the urban community). If you find that in the urban community 20 out of 200 adult women have breast cancer and that in the rural community 10 out of 150 adult women have it, could you conclude, at a significance level of 0.05, that breast cancer is more prevalent in the urban community?1. The parameter of interest is:2. The hypotheses for this test are:3. The calculated test statistic is:4. The critical region is:5. Draw the critical region (make decision):6. It can be concluded that:A Ross MAP team is currently developing a regression model to explain the travel expense of HR consulting firms in a month (measured in thousands of dollars). So far, the team has identified the number of consultants, the number of clients, the number of air-travel trips, and the number of trips to high-expense cities (e.g., NYC, Boston, San Jose) as potential independent variables. A partial output of the corresponding regression model is in Figure 1. Use the figure to answer question 4to6 4. What is the R2 and adjusted R2 of the model? 5. What is the standard error of the estimates (serror) in thousands of dollars? 6. Based on what you can learn from this table, what is your assessment about the model? For your information, the firm with the lowest travel expense was $47K and the firm with the highest expense was $125K in the sample data.Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?
- Data from the Motor Vehicle Department indicate that 80% of all licensed drivers are older than age 25. In a sample of n=50 people who recently received speeding tickets, 33 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use alpha=0.5. A. what is the proposed analysis and why you chose this? B. Test assumptions and make a decision with evidence? C. Inferential statics and P values? D. Final decision and Conclusion?A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…2. An article in the Tappi Journal (March, 1986) presented data on green liquor Na2S concentration (in grams per liter) and paper machine production (in tons per day). The data (read from a graph) are shown as follows: (a) Fit a simple linear regression model with y green liquor Na2S concentration and x production. Draw a scatter diagram of the data and the resulting least squares fitted model.(b) Find the fitted value of y corresponding to x = 910 and the associated residual.
- 8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 21. Prior to being hired, the ve salespersons for a computer store were given a standard sales aptitude test. For each individual, the score achieved on the aptitude test and the number of computer systems sold during the first 3 months of their employment are shown in the attached image. (a) Determine the least-squares regression line and interpret its slope. (b) Estimate, for a new employee who scores 60 on the sales aptitude test, the number of units the new employee will sell in her first 3 months with the company. (c) Find the standard error of estimate. (d) Find the r-square of the model.
- Prove that the slope of the sample regression function (B2) is the blur of the assumption s of gauss Marko theorem are satisfied make sure to show all the steps and the underlying assumptions9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5Consider the simple linear regression model based on normal theory. If we are interested in two different testing H0 : B1 = 0 vs H1: B1 does not = 0 and H0 : p= 0 vs H1: p does not = 0, then show that test statistic value in both the tests are equivalent (values are always same).