Question

Question 7. The results of the correlation analysis in the Correlation Matrix these variables are depicted below. Use information in the table to discuss the strength and nature of relationship between the four variables.

	Training	Performance	Years of Service	Annual Salary
Training	1
Performance	0.016	1
Years of Service	0.377	-0.268	1
Annual Salary	0.597	0.709	0.286	1

Question 9. Results of the three goodness of test measures is given in the table below:

Goodness of Fit Tests
R Square	0.93		ANOVA	F	Sig F
				25.431	0.0008
	Coefficients	St.Error	t Stat	P-value
Intercept	-35.25	7.05	-4.996	0.002
Training	2.47	0.64	3.851	0.008
Performance	8.20	1.20	6.824	0.000
Years of Service	1.1	0.42	2.592	0.041

a) Do the independent variables explain a reasonable amount of variation in the dependent variable? Justify.

  

b) Can any of the independent variables be dropped from the model? Why or why not?

c) Use information in the table to comment on the validity of the model.

Question 10. What recommendation would you provide to Fatima for building the new compensation package?

Question 7. The results of the correlation analysis in the Correlation Matrix these variables are depicted below. Use information in the table to discuss the strength and nature of relationship between the four variables.

	Training	Performance	Years of Service	Annual Salary
Training	1
Performance	0.016	1
Years of Service	0.377	-0.268	1
Annual Salary	0.597	0.709	0.286	1

Answer 1

Problem statement:Test results of a regression model are presented to us. Based on the information present in the tables we have to answer the following questions.

Given: A linear regression model is built to obtain the relationship between annual salary and other independent variables (training, years of service and performance). The model results are presented to us .We have to examine these results and comment on the regression model.

Solution:

(7): Correlation matrix presents the coefficent of correlation between each pair of variables present in the data. Upon close study of the matrix, we observe that performance and annual salary are highly and positively correlated (0.709). Also, we observe that among the independent variables (training, years of service and performance) we do not observe any strong correlation (assuming corrleation value extreme of 0.7 to be highly correlated- Note that decision on the strength of correlation is subjective). We observe that annual salary and training to be positively correlated, but not highly correlated (nearly 0.6). Years of service and performance seems to have a negative association, albeit the association is not too strong (-0.268).

(9a): Yes, independent variables explain a significant amount of variation in dependent varaiable. We can conclude this by referring to the ANOVA table presented in the information.Generally, if p-value associated with F-statistic is less than 0.05, we can conclude that independent variables explain a significant amount of variation in dependent varaiable.

Conceptually, null hypothesis associated with F-statistic is that regression coefficents for independent variables are zero while alternate hypthesis is regression cofficients for independent variables are significantly different from zero. Basically, null hypothesis is- the regression model built using independent variables have impact in explaining variation in dependent variable compared to model without independent variables. When we obtain p-value associated with F-statistic less than 0.05 (Significance level) we conclude that independent variables explain a significant amount of variation in dependent varaiable.

(9b):No, none of the independent variable can be dropped. We conclude that an independent variable can be dropped when the p-value associated with it is greater than 0.05 (generally assumed significance level). Since none of the independent variables have p-value greater than 0.05, we conclude that none of the variables could be dropped.

(9c): To validate this model, we have to refer to the R^{^2} in the model.R square associated with this model is 0.93.  R squared provides the proportion of variation in dependent variable which is attributable to independent variables. A value of 0.93 for R-squared is a good value to validate the model.

Also since the t-statistic associated with all the independent variables have p-value lesser than 0.05, we can validate this regression model.

(10): Based on the regression model, our recommendations for new compensation package is that more importance to be given to the performance of the employees. In the compensation package, second most important variable based on the coefficent value is training. The least important variable to be considered is years of experience while deciding new compensation package.