Question

Question 4 Jenson Tan is the HR manager at company Nilect. As part of his yearly report to the CEO, he is required to present an analysis of the salaried employees. There are over 10,000 employees in Nilect and Jenson does not have sufficient resources to gather information on each salaried employee. As such, he selected a random sample of 30 employees for analysis. For each employee, he recorded monthly salary, service at Nilect in months, years of education obtained, and whether the employee has a technical or clerical job (1-technical job, 0-clerical job) Data collected are shown below:

Answer 1

Regression model : $y=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3x_3+e$

d)To test H0 : $\beta_0=\beta_1=\beta_2=\beta_3=0$ ag. H1 : not H0.
From the ANOVA table, we get the F-value = 25.552.
Critical value = F _0.05;3,26 = 2.975154
Since F > critical value, we reject H0 and conclude that atleast one of the regression coefficients is significant in the regression model.

e) To test H0 : $\beta_3=0$ ag. H1 : not H0.
From the coefficients table, we get the t-value = -1.577.
(Formula for t-stat :
$T=(\hat\beta_3-0)/S.E(\hat\beta_3)=\hat\beta_3/S.E(\hat\beta_3)$ )
Critical value = T _0.05/2;26= 2.055529.
Since |T| < critical value, we accept H0 and conclude that job type is not significant enough in the fitted regression model.