A researcher interviews 50 employees of a large manufacturer and collects data o

Question

A researcher interviews 50 employees of a large manufacturer and collects data on each worker's hourly wage (Wage), years of higher education (EDUC), experience (EXPER), and age (AGE). The data is shown below, the data set can also be found on the text website; labeled Hourly Wage Use Table 4 EDUC EXPER AGE 15.45 6 2 37 26.35 4 18 52 19.15 6 4 4 37.85 11 2 40 21.72 41 39 14.34 4 2 38 21.26 59 53 24.65 6 15 59 2565 6 12 36 15.45 9545 20.39 4 12 37 29.13 5 14 37 27.33 11 3 43 18.02 8 5 32 20.39 9 18 40 24.18 7149 17.29 4 10 43 15.61 1 9 31 35.07 9 22 45 40.33 11 3 31 20.39 4 14 55 16.61 65 30 16.33 9 3 28 23.15 6 15 60 20.39 413 32 14.88 4958 13.88 5 4 28 17.65 654 19.15 6 16.61 6 4 57 18.39 9 3 30 15.45 5 8 43 18.02 7 6 31 13.44 4 3 33 17.66 6 23 51 16.96 4 1537 4.34 49 45 15.45 6 3 55 17.43 5 14 57 35.89 9 16 36 20.39 4 20 60 11.81 4 5 35 1545 9 10 34 17.66 5 4 28 1387 6 1 16.35 7 10 43 15.45 9 2 42 23.67 4 17 47 1602 11 2 46 23.15 4 15 52 24.18 8 11 64 a. Estimate Wage·A+ ,EDUC + AEXPER-MAGE + (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) 1.43 EDUC + 0.45 EXPER + 1 -0.01 AGE b. Choose the appropriate hypotheses to determine whether the influence of experience differs from that of age c. Estimate the restricted model given that the null hypothesis is true (Round your answers to 2 decimal places.) age a 1.34 EDUC +1 0.12 (EXPER + AGE) pe here to search

Explanation / Answer

a) Minitab output:

Regression Equation:

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 3 708.54 236.180 8.02 0.000
Educ 1 530.09 530.095 18.01 0.000
Exper 1 295.82 295.817 10.05 0.003
Age 1 0.31 0.308 0.01 0.919
Error 46 1354.07 29.436
Lack-of-Fit 45 1346.93 29.932 4.19 0.372
Pure Error 1 7.14 7.144
Total 49 2062.61

Model Summary

S R-sq R-sq(adj) R-sq(pred)
5.42552 34.35% 30.07% 18.75%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 7.69 4.10 1.88 0.067
Educ 1.440 0.339 4.24 0.000 1.06
Exper 0.451 0.142 3.17 0.003 1.28
Age -0.0086 0.0836 -0.10 0.919 1.22

Regression Equation

Wage = 7.69 + 1.440 Educ + 0.451 Exper - 0.0086 Age

b) Specifying differe for age:

Answer: B

c)

Regression Analysis: Wage versus Educ, E+A

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 2 540.4 270.18 8.34 0.001
Educ 1 451.3 451.31 13.93 0.001
E+A 1 177.9 177.90 5.49 0.023
Error 47 1522.3 32.39
Lack-of-Fit 39 1288.8 33.05 1.13 0.461
Pure Error 8 233.5 29.19
Total 49 2062.6

Model Summary

S R-sq R-sq(adj) R-sq(pred)
5.69109 26.20% 23.06% 13.75%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 4.98 4.13 1.21 0.234
Educ 1.312 0.352 3.73 0.001 1.04
E+A 0.1388 0.0592 2.34 0.023 1.04

Regression Equation

Wage = 4.98 + 1.312 Educ + 0.1388 E+A

d) Test statistic:

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 3 Wage, Educ, E+A

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 52482 26241.2 323.73 0.000
Error 147 11916 81.1
Total 149 64398

e) Critical value: F (df1,df2, 0.05)= F(2,147,0.05)= 3.0576

f) Answer: A, becuase the test statistic is significant and rejects null hypothesis.

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