[20 marks) The management of a large firm would like to know something about employee morale and the other variables to which it may be related. To study these relationships, each employee in a simple random sample of 23 mm is interviewed and tested to obtain information concerning morale level and the average number of satisfying extra work social contacts experienced during a week. Whether or not the duties the employee usually performs are appropriate to the job title is also determined. The dependent variable Y is measure of morale, the quantitative independent variable, X1 is average number of social contacts, and the following dummy variable coding is used to quantify the qualitative variable: X2 = 1 if yes, X2 = 0 if no. The model including dummy variable and the interaction term was being estimated and a part of computer outputs is below: Y = 131 + 31x1 - 58Xz + 33X1X2 (125) (6.5) (35.1) (15) n 29 F SSE 19950 335560764 55R 54213 Note: SSE 2 SS Explained. SSR = SS Residuals Determine the coefficient of multiple determination and explain it. a b. Determine the adjusted R2 and explain it. .0 Write an equation when the duties the employee usually performs are appropriate to the job title (X2 = 1}. d. Write an equation when the duties the employee usually performs are not appropriate to the job title {X2 = 0). e. You are to test to determine if all the independent variables are jointly significant. With alpha = 0.05, answer the questions. 1) State the null and alternative hypotheses. 2) State the test statistic. 3) What is the degree of freedom?