Monday, January 30, 2012

Example of Regression Questions

Based on the output given, answer the following questions.

(a)        What is your evaluation of the goodness of the model developed?

            R2  = 0.744. So we can conclude that 74.4% of the variation in Sales can be explained by the 4 variables, only about 25.9% variation cannot be explained.

(b)        What can you conclude about the model that was tested?

As the F value = 18.185 and Significant of F = 0.000 < 0.01 so we can conclude that all the 4 variables can explain the variation of the dependent variable. An equation can be formed.

(c)        Test each of the following at the 5% significance level.

[a]                A male salesman will have the same sales volume as a female salesman.
[b]               The higher the anxiety score the lower the sales.
[c]                The more the experience the higher the sales.
[d]               Aptitude has a positive relationship with sales.

H0      b1   =  0
H1      b2   ¹  0

Variable                 t value             p value                                     Decision

Gender                  4.066               0.000               p < 0.05           Reject H0

H0      b2   =  0
H1      b2   <  0

Score                     0.844               0.406               p > 0.05           Accept H0
H0      b3   =  0
H1      b3   >  0

Experience                        2.494               0.020               p < 0.05           Reject H0

H0      b4   =  0
H1      b4   >  0

Aptitude                2.076               0.048               p < 0.05           Accept H0

(d)       What is the difference in the sales of a female salesman compared to a male salesman?
            Lower by RM 13150

(e)        Are all the assumptions of the regression fulfilled (Support your answer by using the values or charts given in the output)? If not please explain how they can be tested?

·         No multicollinearity problem as VIF<10 and Tolerance>0.1.
·         No autocorrelation as the D-W = 1.650.
·         P-P plot shows the errors are normally distributed
·         No problem of Hetrocedascity. Variance is constant (Plot studentized residual and dependent)

(f)        Give suggestions to Pam on how she can increase the sales of her company.
            From the analysis gender, aptitude and experience are significant predictors. Pam should take more salesperson with higher aptitude scores and also with more number of years experience. The company should not waste time on the anxiety test as it is not a significant predictor of sales. Male salesperson also has show that they can do more sales compared to female salespersons.

 Thank you to Prof Ramayah.

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