Question

QUESTION #2

The set of data below shows a random sample of 14 systems analysts who were surveyed in 1978.

                                                Years of

Sampled      Years in                Post-secondary                         Annual Pay

Person        Experience            Education             Gender        in $1,000s  

A                          5.5              4.0                        F                 29.9

B                          9.0              4.0                        M                35.5

C                          4.0              5.0                        F                 33.9

D                          8.0              4.0                        M                34.0

E                          9.5              5.0                        M                32.5

F                           3.0              4.0                        F                 30.5

G                          7.0              3.0                        F                 31.0

H                          1.5              4.5                        F                 27.7

I                            8.5              5.0                        M                40.0

J                           7.5              6.0                        F                 35.0

K                          9.5              2.0                        M                31.0

L                           6.0              2.0                        F                 28.6

M                         2.5              4.0                        M                30.0

N                          1.5              4.5                        M                27.5

A MULTIPLE REGRESSION WAS RUN. Note that Male/Female – the gender variable was given dummy symbols as Female = 1 and Male = 0, or vice-versa.

MULTIPLE REGRESSION ANALYSIS

The set of data above shows a random sample of 14 systems analysts who were surveyed in 1978.

                                                Years of

Sampled      Years in                Post-secondary                         Annual Pay

Person        Experience            Education             Gender        in $1,000s  

A                          5.5              4.0                        F=1             29.9

B                          9.0              4.0                        M=0            35.5

C                          4.0              5.0                        F=1             33.9

D                          8.0              4.0                        M=0            34.0

E                          9.5              5.0                        M=0            32.5

F                           3.0              4.0                        F=1             30.5

G                          7.0              3.0                        F=1             31.0

H                          1.5              4.5                        F=1             27.7

I                            8.5              5.0                        M=0            40.0

J                           7.5              6.0                        F=1             35.0

K                          9.5              2.0                        M=0            31.0

L                           6.0              2.0                        F=1             28.6

M                         2.5              4.0                        M=0            30.0

N                          1.5              4.5                        M=0            27.5

RESULTS – COMPUTER OUTPUT

                       SYSTEMS ANALYSTS ANNUAL PAY

                   REGRESSION FUNCTION & ANOVA FOR PAY

   PAY = 20.8779 + 0.801571 EXPRC + 1.595737 EDUC - 0.382572 GENDER

   R-Squared                          = 0.675011

   Adjusted R-Squared         = 0.577514

   Standard error of estimate = 2.251716

   Number of cases used       = 14

                          Analysis of Variance

   Source             SS                   df         MS            F Value        Sig Prob

                                                                                                p-value

   Regression    105.30990         3        35.10330      6.92342     0.008376

   Residual       50.70225          10      5.07022

   Total           156.01210         13

                       SYSTEMS ANALYSTS ANNUAL PAY

                     REGRESSION COEFFICIENTS FOR PAY

                                                                       Two-Sided p-value

     Variable           Coefficient    Std Error      t Value     Sig Prob

     Constant           20.87790      3.06815      6.80472     0.000047

     EXPRC           0.80157      0.22847      3.50845     0.005646

     EDUC               1.59574      0.56064      2.84626       0.017361

     GENDER         -0.38257      1.28741     -0.29716     0.772423 *

     * indiciates that the variable is marked for leaving

     Standard error of estimate = 2.251716

     Durbin-Watson statistic    = 2.487978

Use the above computer output to answer the question below

What is the estimated multiple regression?

ANSWER

At a level of significance of ? = 0.05, which variables are statistically significant and which ones are not statistically significant?

ANSWER

Explain the meaning behind R-Squared in this problem

ANSWER

Does the output point to gender discrimination in pay? Why or why not?

ANSWER

Answer 1

What is the estimated multiple regression?

The estimated multiple regression equation for the given regression model is given as below:

Estimated PAY = 20.8779 + 0.801571 *EXPRC + 1.595737 *EDUC - 0.382572 *GENDER

At a level of significance of ? = 0.05, which variables are statistically significant and which ones are not statistically significant?

The P-value for significance of the regression coefficient for the variable experience in years is given as 0.005646 which is less than ? = 0.05, so it is indicate that the variable experience in years is statistically significant.

The P-value for significance of the regression coefficient for the variable years of post secondary education is given as 0.017361 which is less than ? = 0.05, so it is indicate that the variable years of post secondary education is statistically significant.

The P-value for the significance of the regression coefficient for the variable gender is given as 0.772423 which is greater than ? = 0.05, so it is indicate that the variable gender is not a statistically significant variable.

Explain the meaning behind R-Squared in this problem

The value for the R squared or coefficient of determination for the given regression model is given as 0.675011, which means about 67.50% of the variation in the dependent or response variable annual pay is explained by the explanatory or independent variables experience in years, years of post secondary education, and gender.

Does the output point to gender discrimination in pay? Why or why not?

No, given output do not point out the gender discrimination in pay, because the variable gender is not statistically significant as per given regression output.