2. Analyze the Bonus Eligibility variable. a. (6 points) Write a short managerial summary characterizing the fraction of executives in the population who are likely to be bonus eligible and your uncertainty surrounding it. b. (2 points) One of our senior executives thinks, based on his prior experience, that that the true fraction of executives who are eligible for a bonus is actually 70%. What can you say about his claim? Explain your reasoning. 3. (5 points) Generate a scatterplot for Salary (y) vs. Experience (x) and fit a line to the data. Is the anomalous point an outlier? High leverage? High influence? Explain why in 1 sentence. ID #117 of the dataset contains a typo from someone misreading a 2 as a 5 for the experience variable. ID# 117's Experience should be = 24 years. Fix this only AFTER answering Q#1-3. YOU WILL LIKELY FAIL THE EXAM IF YOU DON'T FIX THIS. 4. Dr. Gupta asks you to build a model to predict salary. To begin with, start with Years of Experience as a predictor, and model the relationship. Don't forget to fix the point that was an error. a. (5 points) Write a summary of the model results that includes your assessment of whether the model is a good model, whether experience predicts salary, uncertainty, and other managerially relevant issues. You may paste a managerially relevant graphic if that helps explain your answer . b. (3 points) Your manager suggests that the relationship between experience and salary might be different for those who are eligible for a bonus than for those not eligible. How would you check for this? Note: explain the exact process you would follow, but you do not need to run this analysis. 5. In the questions below, you will attempt to build a better model to predict salary. a. (12 points) Construct a model to predict salary using as many of the other variables as you think should be used to predict salary. Justify your answer, explaining whether this is a good model or not. Write a managerial summary of your model results. Note, a client is particularly interested in the effects of each variable on salary, so be sure to include those interpretations. Also, please paste the entire table of parameter estimates (i.e., the slopes/coefficients and p- values) so that Dr. Gupta can see the technical results. b. (3 points) Compare two executives who have 12 versus 17 years of experience, respectively. Holding other things constant. based ur fitted how ore/less would you\fYou have been hired by Hay Compensation, Inc, whose business model is to use data to help rms set salaries. Hay has collected data consisting of a simple random sample of 100 managers, which can be found in the Manager Salary dataset, The variables are described below. As a matter of corporate policy, Hay Inc. expresses uncertainty using 95% condence and an a = .05 unless otherwise noted. Write all answers l0 your manager; Dr. Lalitha Gupta, who is both an MBA and a Ph.D. in engineering. She wants to see both managerial relevance (to Show that you can writefor clients) and technical backup (to Show that she should trust you). ID Employee ID number SALARY Salary (dollars) EXP Experience (years) EDU Education (years) BONUS Bonus Eligibility (0 = not eligible, l = eligible) SUPER Number of employees supervised ASSETS Corporate assets {millions of dollars) BOARD Board member (1 = Yes, 0 = No) AGE Age (years) ENTERNAT Has international responsibility (I = Yes, 0 = No) l. Summarize the distribution of salaries (Salary). a. (6 points) Write a managerial sunnnary of the distribution of salaries. Be sure to both summarize the distribution and to provide your manager with a condence interval for the mean salary. Interpret your condence interval in terms your client can understand. You may include any graphic appropriate for a manager that you think would aid in understanding. b. (2 points) One of the firm's executives thinks that the mean salary of executives like these is $110,000 per year. What would you tell him based on the data? 2. Analyze the Bonus Eligibility variable. a. {6 points) Write a short managerial summary characterizing the fraction of executives in the population who are likely to be bonus eligible and your uncertainty surrounding it. b. (2 points) One of our senior executives thinks, based on his prior experience, that that the true