(a) Explain why you would or wouldn\'t agree with each of the following statemen
ID: 3250622 • Letter: #
Question
(a) Explain why you would or wouldn't agree with each of the following statements: (i) Cov(X, Y), and Corr(X, Y) can take values between -infinity and +infinity. (ii) If Cov(X, Y) = 0 and Corr(X, Y) = 0, one can conclude that there is no relationship between X and Y. (iii) The least squares line fit to the points in the scatter plot of Y versus the fitted values Y has a zero intercept and a unit slope. (b) When answering the question, carefully state any additional assumptions you need to make and clearly define any new notation you introduce. Suppose that in the population the annual salary (Salary) of a CEO (Chief Executive Officer) measured in hundreds of thousands of dollars is related to the annual sales of the company (Sales) measured in hundreds of thousands of dollars according to the following regression model: Salary_i = 5 + 0.1 Sales_i + element_i where the element_i are iid, independent of Sales, and element_i ~ N (0, 9) and Sales_1 ~ N (50, 10). (i) What is the standard deviation of CEO salaries for CEOs of firms with annual sales of five million dollars? (ii) What is the expected difference between the salary of CEO of a firm with five million dollars in annual sales and the CEO of a firm with annual sales of eight million dollars? (iii) Give a 95% level confidence interval for the difference in salary between the CEO of a firm with five million dollars in annual sales and the CEO of a firm with eight million dollars in annual sales? (iv) What is the population average of CEO salary? (v) Suppose you have a sample of 1000 observations from the population described above. Will 0.1 be in the 95% confidence interval for the slope obtained in this sample? Explain your answer. (No marks will be awarded without an explanation.)Explanation / Answer
a) i) Covariance is a measure of how much two random variables vary together. However the Correlation explains the
linear relationship between two random variables. So the value of correlation lies betwwen 1- to +1 as it indicate the percentage of linear relationship. if it is perfect positive value is +1, perfect negative value is -1, no correlation value=0.
ii) Cov(X,Y) =0 and Corr(X,Y)=0 we con conclude that there is no linear relationship between this two variable.
if one variable changes one can not say about the other variable.
iii) A least square line fit to the points in the scatter plot Y versus fitted value of Y has zero intercept and unit slope,
it indicate the perfect positive relationship between this two values.
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