Question

Suppose you need to examine the relationship between wages (in $1,000) and the variables: experience in the field (Exper), number of academic degrees (Degrees), and number of previous jobs in the field (Prevjobs). Experience in the field is measured in years.

You took a sample of 20 employees and obtained the following output ( Must show your work otherwise you get half credit):

                         Coeff                   StdError              t Stat              p-value

Intercept               -7.23                     2.52                 -2.87               0.011

Exper                   -0.15                     0.18                ?????                 0.41

Degrees                 ????                     0.80                    9.1               0.000

Prevjobs               -0.65                     0.52                   -1.25               ????

a)  Compute the t statistic for the experience in the field (Expr).                                                    

b)  Interpret the coefficient for Expr.  Is it reasonable?                                                                 

c) Compute the coefficient  for the number of academic degrees (Degrees)                               

d) State the multiple regression equation.                                                                                       

e) Estimate the p_value of the number of previous jobs in the field (Prevjobs)                        

        

f) Interpret the coefficient of multiple determination    (R_square)                                               (3  marks)

g) Predict the wage for a person with 6 years of experience, 3 degrees, and 2 previous jobs (interpret the results).                                                                                                                                                                                                           

  

h)  Use the p_values to confirm which variables are significant at α=0.05?  (do not conduct the 5 steps. Just state why).                                                                                                           

Answer 1

Let the estimated multiple linear regression line is:

y: wages in thousand $

x₁: number of years of experience

x₂: number of academic degrees

x₃: number of previous jobs

If we want to test the significance of any regression coefficient we use the following testing procedure.

versus   

Test statistic:

under H₀ the test statistic follows t-distribution with n-1 degrees of freedom.

where n is the sample size. n = 20

(a) -

t-statistic for experience in the field =

(b) -

Coefficient of experience is -0.15. This means if the employee has an extra year of experience then he is expected to get 0.15 times less wages, given that rest of the variables are kept constant. This does not seem reasonable, because if the employee has more years of experience then he should get the wages increased.

(c) -

t-statistic for number of academic degrees =

Coefficient of number of academic degrees is 7.28

(d) -

Multiple linear regression equation is :

(e) -

P-value = P[ |t₁₉| > |T| ]

P-value for the number of previous jobs in the field = P[ |t₁₉| > 1.25] = 2*P[ t₁₉ > 1.25] = 0.2265

(f) -

Coefficient of multiple determination gives the percentage of total variation in the values of dependent variable is explained by the regression model.

If the coefficient of multiple determination is r, then 100r% of the total variation is explained by the model.

(g) -

Given, number of years of experience = x₁ = 6

number of academic degrees = x₂ = 3

number of previous jobs = x₃ = 2

Predicted wages is $12.41 thousand.

(h) -

We reject the significance of regression coefficient at level of significance if p-value < 0.05

Here, only p-value of number of academic degrees is less than 0.05.

Hence, at 0.05 level of significance only the number of degrees of freedom is significant.

I hope you find the solution helpful. Feel free to ask any doubt in the comment section.

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