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(a) Use the built regression tool in Excel and your personalized data set (see above) to estimate the simple regression of sales revenue in dollars (...
(a) Use the built regression tool in Excel and your personalized data set (see above) to estimate the simple regression of sales revenue in dollars (Y) generated by a salesperson in his/her first year of completed service on the salesperson's aptitude test score (X). (2 marks)
When answering the following questions, assume all the assumptions of the neoclassical (stochastic regressor) simple regression (NSR) model with multivariate normally distributed random disturbances are satisfied.
(b) Clearly state your estimated conditional expectation function (sample regression line). Note that you do not need to estimate your equation manually, but rather you should simply write down your sample regression line using the estimated intercept and coefficient of X given in your summary regression output from Excel. (1 mark)
(c) With reference to your estimated equation, calculate (using a calculator) a 90% confidence interval for the coefficient (β2 ) of X in the model. In performing this
calculation, use the relevant estimated standard error of the estimator of the coefficient of X given in your summary Excel regression output. Give an interpretation of the confidence interval you calculate. (2 marks)
(d) Again with reference to your estimated equation, perform a test of the null hypothesis that the coefficient (β2 ) of the aptitude test score of a salesperson equals zero against
the alternative that it is greater than zero, using the α = 0.05 (i.e. 5%) level of significance. In presenting your answer to this question you are required to use the 6- step hypothesis testing procedure given in the unit summary lecture notes. Again in answering this question, you should use the relevant estimated standard error of the estimator of the coefficient of X given in your summary Excel regression output. (3 marks)
(e) Give an interpretation of the realized coefficient of determination value (r2 ) given in your summary Excel regression output. (2 marks)
