Extracted text: (2). We would like to do a F test of goodness of fit for the whole equation. Please demonstrate your answer. (Note: at 5% significance level, the critical value of F statistic is: F(4,180)=2.42, F(4,181)=2.43, and F(5,180)=2.26) (3) How to test whether there is a gender differentiation in the impact of earnsie and ageie on contrib;ie at the same time ? Specifically, (i) Please write out the new model you would like to estimate. (ii) Please write out the null hypothesis. (iii) Please write out the test statistic (Hint: The goal of this question is to examine interactive term and F test relating to groups of explanatory variables)
Extracted text: 6. Government initiated a new pension program, in which employees are allowed to determine his/her annual pension contribution ratio. To investigate what factors will affect the decision on contribution ratio, researcher surveyed 185 employees coming from 10 firms and set up the following regression model. contrib, = Bo + Bearns, + B,age, + Bmale + B,mrate, + ue (1) Where, i denotes firm; e denotes employee; contrib, denotes firmi employee e's annual pension contribution ratio; earns denotes the employee's annual income; age denotes the age of employee e;male is a dummy variable, with value of 1 if the employee is male, 0 otherwise; mrate, denotes the pension contribution ratio made by firm i; u denotes the disturbance term. This model is satisfying the six assumptions for classic linear regression model. OLS estimation results are reported as follows (standard errors are reported in the parentheses) : contrib,e = 0. 12 + 0.24earnsie + 1.2ageie - 2.46maleie + 0.66mrate; (0.06) (0.06) (0.31) (0.50) (0.12) R2 = 0.40 n = 185