2. The salaries of 100 employees in an IT company have been collected. Along with their annual salaries in dollars), the years that the employees have worked for the company as well as their genders are also recorded Three models have been fitted with relevant R outputs shown below. > ft bc logftk logft2 anova (logft2, logft1) Analysis of Variance Table Model 1: log(salary) years Model 2: log(salary) - years + factor(gender) Res. Df RSS Df Sum of SqF Pr(>F) 1 1 98 3.7439 2 97 3.7140 1 0.029905 0.781 0.379 > summary(logft2) Call: Im(formula - log(salary) years) Coefficients: Estimate Std. Error t value Pri> | (Intercept) 10.48381 0.04108 255.18 rs plot(years,rs) > abline (h=) > qqnorm(rs) Normal Q-Q Plot d o o o go 10 og O 28 000 Sample Quantiles 808 000 0 oo 8 OO 08 00 g oo og 00 O 26 o o -2 5 5 10 15 20 25 -1 0 1 2 Theoretical Quantiles years (a) Describe carefully the two models in ft and in logfti. Explain why the latter is preferable than the former one. [9 marks] (b) Based on the outputs presented above, is there statistical evidence that there is a disparity between the salaries of the male and female employees? [7 marks] (c) Give an estimate for the salary of a female employee with 10 years' experience in the company. [5 marks] (d) What is the predictive power test for the model fit in logft2? Comment on the result of this test. [4 marks] e) Do the data support the assumptions of the linear model? Explain your reasons. [5 marks