ADM XXXXXXXXXXAssignment 1 1 ADM XXXXXXXXXXASSIGNMENT 4 [30 points] Due Date: Sunday, April 7th, 2019, before 11:30 pm Instructions: 1. Your assignment should be uploaded to Brightspace in pdf format....

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ADM 2304 - Assignment 1 1 ADM 2304 -- ASSIGNMENT 4 [30 points] Due Date: Sunday, April 7th, 2019, before 11:30 pm Instructions: 1. Your assignment should be uploaded to Brightspace in pdf format. 2. You may use Minitab or other software for any calculations. However, you must show your manual calculations when asked. 3. Whenever you perform a hypothesis test, use a 5% significance level. 4. Remember to include your integrity statement. 1. [15 points] We are interested in the relationship between the compensation of Chief Executive Officers (CEO) of firms and the return on equity of their respective firm, using the dataset salary.xlsx. The variable salary shows the annual salary of a CEO in thousands of dollars, so that y = 150 indicates a salary of $150,000. Similarly, the variable ROE represents the average return on equity (ROE) for the CEO’s firm for the previous three years. A ROE of 20 indicates an average return of 20%. a) Draw a boxplot and a histogram of the salary of CEO. Are there any apparent outliers in the data? Are there high leverage points? b) Use your software to estimate the relationship and report your results. ??????? = ?0 + ?1???? + ?? c) Looking at a plot of the residuals against predicted values and at the normal probability plot of residuals, does the estimated model appear satisfactory? d) Use your software to estimate the model, this time by using the database salaryalt.xlsx which excludes all the data points for which the salary of the CEO appears extraordinarily large considering the ROE of their firm. Report your results. e) Produce a histogram and a normal probability plot of the residuals of this regression. Does this regression appear to meet the conditions of absence of outliers and near normality? f) What are the units of the slope coefficient b1 in this equation? What is the impact on the salary of the CEO of firm i if the ROE increases by 1%? g) Use your results to calculate a 95% interval to estimate the mean salary of CEOs whose firms have an ROE of 20 per cent. 2 2. [15 points] We are interested in measuring the impact of years of education on the hourly wage individuals. Using the dataset wage.xlsx, we propose to investigate this question by estimating the following model, where ln(wage) is the natural log of the wage variable. ln(wage?) = ?0 + ?1????? + ?2?????? + ?3??????? + ?? In the database, the variable wage is the wage in $ per hour and the variable lwage is the natural log of the wage variable. Educi measures the number of years of education, experi measures the number of years in the labour force and tenurei measures the number of years of work with current employer. a) Draw a histogram of the wage variable, and compare it to a histogram of ln(wage). Based on this comparison, comment on the appropriateness of using ln(wage) as the dependent variable, instead of just wage. b) Would you expect the variables educ, exper and tenure to contribute positively or negatively to the wage of individuals? Justify very briefly your answer. c) Using your statistical software, obtain and present coefficient estimates for all the parameters of the model. Looking at a normal probability plot of the residuals and at a scatter plot of the regression residuals against predicted values, do the conditions of equal variance and the near normality assumption appear satisfied? d) Test if the regression model is useful. or any good at all. e) Test whether the tenure variable is a useful addition to the model. f) What is the estimated impact on wages if there is an additional year of education? You suspect there might be some hidden non-linearity in your data, so you decide to estimate the equation ln(wage?) = ?0 + ?1????? + ?2?????? + ?3?????? 2 + ?4??????? + ?? g) Using the Adjusted R2 criteria, does the addition of exper2 in the equation improves the quality of the model? Explain why it is appropriate to use the Adjusted R2 and not the simple R2 to determine if the addition of this new variable improves the model. h) Explain if multicollinearity is an issue for this model. i) Calculate a 95% interval to predict the wage of a person with 12 years of education, 10 years experience, and 5 years tenure. Think carefully how you would handle the quadratic term.