I need manual calculations done for the statistic problems in the attached file.
STA Baruch College, STA 4155 Final, Spring 2021 Page 1 Before taking the exam, WRITE the following statement: “I will neither give nor receive unauthorized assistance on this exam.” and SIGN your name. Failing to do so may result in a grade of zero. 1. A hospital administrator wished to study the relation between patient satisfaction (??) and patient’s age (??1, in years), severity of illness (??2, an index), and anxiety level (??3, an index). Data were collected on randomly selected 46 patients, where larger values of ??, ??2, and ??3 are, respectively, associated with more satisfaction, increased severity of illness, and more anxiety. A multiple regression model was fitted to the data. The R output is given below. (A) (4 points) Write the fitted regression equation. (B) (4 points) Interpret the coefficient of ??3 (anxiety level) in the context of the problem. (C) (6 points) Compute a 95% confidence interval for ??3. (D) (8 points) Check the model assumptions based on the two plots of the studentized residuals. Now, given below is an ANOVA table produced by R. Baruch College, STA 4155 Final, Spring 2021 Page 2 (E) (6 points) Find ??????, ??????, and ??????. (F) (6 points) Compute ??2 and ????2. (G) (3 points) Compute the residual standard error ???? . (H) (8 points) Test whether there is a overall linear association between the response and the three predictors using ?? = 0.05. State the hypotheses, compute the ?? test statistic, find the p-value, and draw your conclusion. The following table gives the values of ??2 and ?????? for different subsets of predictor variables included in the regression model. Predictors in model ??2 ?????? None 0 262.916 ??1 .6190 220.529 ??2 .3635 244.131 ??3 .4155 240.214 ??1, ??2 .6550 217.968 ??1, ??3 .6761 215.061 ??2, ??3 .4685 237.845 ??1, ??2, ??3 .6822 216.185 (I) (6 points) Which subset of predictor variables you would recommend as the best for predicting patient satisfaction according to ??2 and ??????, respectively? Justify. (J) (5 points) If a backward elimination procedure were used to determine the best subset of variables based on the ?????? criterion, briefly state the steps in the context of the problem based on the ?????? values in the above table. 2. In a study of innovation in the insurance industry, an economist wishes to relate the speed with which a particular insurance innovation is adopted (??) to the size of the insurance firm (??1) and the type of firm. The response variable is measured by the number of months elapsed between the time the first firm adopted the innovation and the time the given firm adopted the innovation. The size of firm is measured by the amount of total assets of the firm. The type of firm is a categorical variable composed of two levels—stock companies and mutual companies. An indicator is defined to represent this variable: ??2 = 1 if stock company and = 0 if mutual company. Then, a linear model, ?? = ??0 + ??1??1 + ??2??2 + ??3??1??2 + ??, is fitted to the sample data. The R output is given below. (A) (3 points) How many firms are included in the study? Explain. (B) (8 points) Interpret the coefficients ??0, ??1, ??2, and ??3 in the context of the problem. Baruch College, STA 4155 Final, Spring 2021 Page 3 (C) (8 points) Using ?? = 0.05, test whether the interaction term can be dropped. State the hypotheses, the value of test statistic, p-value, and your conclusion. (D) (5 points) Based on the output, is it able to test whether both ??2 and ??1??2 can be dropped simultaneously using ?? = 0.01? If so, perform the test; otherwise, explain. (E) (4 points) If the type of firm were composed of ?? levels (?? > 2), how would you include this categorical variable in the regression model? 3. Given below is the time series plot of the monthly sales of red wine (in kiloliters) by Australian winemakers from January 1980 to August 1991. Also, the monthly sales in 1991 are given: (A) (6 points) Based on the time series plot, which components are present in this time series? Are there any other noteworthy features? (B) (4 points) Use an MA(3) smoother to forecast the sale for September 1991. (C) (4 points) The actual sale for September 1991 was 2617. Find the absolute percentage error for the month. (D) (2 points) Which will be smoother, a 3-month moving average or a 12-month moving average?