a) Regression models use the method of "least squares" to estimate the coefficients. Explain the concept of "least squares" and outline how the estimated parameters are derived. (4 marks) b) Consider the dependent variable ChangeRev i. If an employee has a positive value for this variable, what does that mean? (2 marks) ii. The mean of ChangeRev for this sample was $880.65. What does this value suggest?' (2 marks) iii. The 95% confidence interval for the mean of ChangeRev is ($791.19, $970.10). With reference to the population and the sample explain what a 95% confidence interval means. (3 marks) iv. If we had calculated a 99% confidence interval would it have been wider or narrower than the 95% interval? (1 mark) v. It has been pointed out that you should take account of inflation when interpreting the mean of ChangeRev. What relevance would inflation have, and what difference would it make to interpreting the mean value? (4 marks) c). Let us now explain and interpret the multiple regression coefficients, including the intercept. i. State and interpret the intercept. (2 marks) ii. State and interpret the coefficient on LowPrevRev. (2 marks) iii. State and interpret the coefficient on Children. (2 marks) d) Perform a relevant hypothesis test on the coefficient of the variable Female and explain what the outcome of the test means in the context of this initiative. (4 marks) e) Consider the use of this regression model for prediction. i. Use the model above to predict the revenue six months after the course for a female employee with no children, who generated $180 revenue the month before taking the course