MGSC2301 PROJECT #4 (Regression Analysis) complete solutions correct answers key

MGSC2301 PROJECT #4 (Regression Analysis) complete solutions correct answers key

This project again utilizes the data set for the Bank and Trust Company (B&T); the random sample of 222 employees and data recorded for several variables:

·     Annual salary earned by the employee; 

·     The age of the employee;

·     The years of experience in the banking industry held by the employee prior to

        joining B&T;

·     The education level of the employee;

·     The extent to which the employee uses a computer;

·     The grade classification within B&T held by the employee;

·     The years of experience at B&T;

·     The gender of the employee;

·     The citizenship of the employee; and

·        A location adjustor for salary using a 1-5 scale.

Assume that you still work for Ms. Deanna V. Ashun (aka “Dee”) and she is now most concerned about finding that set of variables which truly relate to annual salary (e.g, EDUCATION LEVEL probably is correlated with salary, whereas CITIZENSHIP is probably not).

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Ms. Ashun has certain suspicions, but is not absolutely sure which variables are the most important in terms of the salaries paid at B&T.  She decides to exclude the CEO from all calculations and use the following notation:

                     y = Annual salary paid in $1000s

                     x1 = Age in years

                     x2 = Years of experience prior to B&T

                     x3 = Level of education; x3 = 1,2,3,4,5

                     x4 = 0/1 variable for computer usage

                     x5 = Job classification; x5 = 1,2,3,4,5,6

                     x6 = Years of experience at B&T

                     x7 = Gender; 0 à Male; 1 à Female

                     x8 = Citizenship (but this is nominal data, so will not be used here)

                     x9 = Salary adjustor for location; x9 = 1,2,3,4,5

 (a)     After some thought, she decides that PRIOR, EDUC, GRADE, EXPERI and

           GENDER are probably those variables which correlate most highly with

SALARY.  Assuming that all relationships are linear (i.e., of the form

E(y) = b0 + b1xi), she asks you to complete the following table (please put your answers on the Yellow Sheet):

           (10 points)

Dep. Variable

Ind. Variable

                                 Prediction Equation

  R² value

   SALARY

 PRIOR

   y = _______________ + ________________ * PRIOR

   SALARY

 EDUC

   y = _______________ + ________________ * EDUC

   SALARY

 GRADE

   y = _______________ + ________________ * GRADE

   SALARY

 EXPERI

   y = _______________ + ________________ * EXPERI

   SALARY

 GENDER

   y = _______________ + ________________ * GENDER

(b) 1. Are the sings of the slops as expected? 2. Interpret each slope coefficient:                      (8 points)

PRIOR:

EDUC:

GRADE:

EXPERI:

 (c)     Of the five variables, which two have the highest R² values?

           (1 point)

r PRIOR r  EDUC          r  GRADE r  EXPERI           r  GENDER

           Of the five variables, which two have the lowest R² values?

           (1 point)

r PRIOR r  EDUC          r  GRADE r  EXPERI           r  GENDER

Now aware that GRADE has the single greatest impact on SALARY, Ms. Ashun wonders what variables influence GRADE.  She suspects that greater academic credentials are needed to get promoted to the higher ranks at B&T, and further suspects that this relationship is linear.  Thus, for all employees in the sample (excluding the CEO), she asks you to investigate the following model:

                                                                                     GRADE = b0 + b1*EDUC

(d)      Get the full regression output for this model.  

           d1.      Specify the final prediction equation:

                     (3 points)

           d2.      What percent of the variance in GRADE is due to factors other than

                     EDUCation?

                     (3 points)

           d3.      What is the 95% confidence interval for the slope of your model?

                     (3 points)

           d4.      Assuming your reader is Mr. Pellsize (intelligent non-statistician),

                     explain the numeric values found in part (d3) in one or two sentences.

                     (3 points)

Ms. Ashun also knows that using this regression model to make predictions about GRADE means that at least there assumptions must be satisfied:

·        The errors terms must follow a normal distribution; and

·        Error values are statistically independent; and

·        The variance of the error terms must be relatively constant.

(e)       Generate both a residual plot as well as the normal probability plot.

           Please attach these two plots to this paper.

           (6 points)

(f)       Based on your plots, do you believe that the errors terms follow a normal            distribution?

           (1 point)

           Justify your answer from this part.

           (3 points)

(g)     Based on your plots, do you believe that the error values are statistically independent?

           (1 point)

           Justify your answer from this part.

           (3 points)

(h)      Based on your plots, do you believe that the variance of the error term is constant?

           (1 point)

           Justify your answer from this part.

           (3 points)

NAME(S):                         _____________________________________

                                          _____________________________________

                      _____________________________________

SCORE (out of 50):                     ______________________

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(a)

Dep. Variable

Ind. Variable

                                 Prediction Equation

  R² value

   SALARY

 PRIOR

   y = _______________ + ________________ * PRIOR

   SALARY

 EDUC

   y = _______________ + ________________ * EDUC

   SALARY

 GRADE

   y = _______________ + ________________ * GRADE

   SALARY

 EXPERI

   y = _______________ + ________________ * EXPERI

   SALARY

 GENDER

   y = _______________ + ________________ * GENDER

(b) 1. Are the sings of the slops as expected? 2. Interpret each slope coefficient:                      

PRIOR:

                     _____________________________________________________

                     _____________________________________________________

EDUC:         _____________________________________________________

                     _____________________________________________________

GRADE:       _____________________________________________________

                     _____________________________________________________

EXPERI:       _____________________________________________________

                     _____________________________________________________

(c)       Two highest R² values:

r PRIOR r  EDUC          r  GRADE r  EXPERI           r  GENDER

           Two lowest R² values:

r PRIOR r  EDUC          r  GRADE r  EXPERI           r  GENDER

(d)      d1.      Prediction equation:

                      GRADE = __________________ + ____________________*EDUC

           d2:      Percent variance due to other factors = _________________________

           d3.      95% Confidence Interval for slope = ( ____________, ____________ )

           d4.      Interpretation of (d3):

                     _____________________________________________________

                     _____________________________________________________

(e)       Generate both a residual plot as well as the normal probability plot.

           Please attach these two plots to this paper.

(f)       Error terms follow a normal distribution?                 r YES       r       NO

           Justification of your answer:

                     _____________________________________________________

                     _____________________________________________________

(g)      Are error values statistically independent?                 r YES       r       NO

           Justification of your answer:

                     _____________________________________________________

                     _____________________________________________________

(h)      Error terms show constant variance?                           r YES              r NO

           Justification of your answer:

                     _____________________________________________________

                     _____________________________________________________