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).

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  Male; 1  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

STATS250 PROJECT #3 (Regression Analysis) Page 2

(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) = 0 + 1xi), 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:

STATS250 PROJECT #3 (Regression Analysis) Page 3

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

 PRIOR  EDUC  GRADE  EXPERI  GENDER

Of the five variables, which two have the lowest R2 values?
(1 point)

 PRIOR  EDUC  GRADE  EXPERI  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 = 0 + 1*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)
STATS250 PROJECT #3 (Regression Analysis) Page 4

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)

c) Two highest R2 values:

 PRIOR  EDUC  GRADE  EXPERI  GENDER

Two lowest R2 values:

 PRIOR  EDUC  GRADE  EXPERI  GENDER

(d) d1. Prediction equation:

GRADE = __________________ + ____________________*EDUC

STATS250 YELLOW SHEET FOR: PROJECT #3 Page 3

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?  YES  NO

Justification of your answer:

_____________________________________________________

_____________________________________________________

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

Justification of your answer:

_____________________________________________________

_____________________________________________________

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

 

 

 

Sample Solution

Sample solution

Dante Alighieri played a critical role in the literature world through his poem Divine Comedy that was written in the 14th century. The poem contains Inferno, Purgatorio, and Paradiso. The Inferno is a description of the nine circles of torment that are found on the earth. It depicts the realms of the people that have gone against the spiritual values and who, instead, have chosen bestial appetite, violence, or fraud and malice. The nine circles of hell are limbo, lust, gluttony, greed and wrath. Others are heresy, violence, fraud, and treachery. The purpose of this paper is to examine the Dante’s Inferno in the perspective of its portrayal of God’s image and the justification of hell. 

In this epic poem, God is portrayed as a super being guilty of multiple weaknesses including being egotistic, unjust, and hypocritical. Dante, in this poem, depicts God as being more human than divine by challenging God’s omnipotence. Additionally, the manner in which Dante describes Hell is in full contradiction to the morals of God as written in the Bible. When god arranges Hell to flatter Himself, He commits egotism, a sin that is common among human beings (Cheney, 2016). The weakness is depicted in Limbo and on the Gate of Hell where, for instance, God sends those who do not worship Him to Hell. This implies that failure to worship Him is a sin.

God is also depicted as lacking justice in His actions thus removing the godly image. The injustice is portrayed by the manner in which the sodomites and opportunists are treated. The opportunists are subjected to banner chasing in their lives after death followed by being stung by insects and maggots. They are known to having done neither good nor bad during their lifetimes and, therefore, justice could have demanded that they be granted a neutral punishment having lived a neutral life. The sodomites are also punished unfairly by God when Brunetto Lattini is condemned to hell despite being a good leader (Babor, T. F., McGovern, T., & Robaina, K. (2017). While he commited sodomy, God chooses to ignore all the other good deeds that Brunetto did.

Finally, God is also portrayed as being hypocritical in His actions, a sin that further diminishes His godliness and makes Him more human. A case in point is when God condemns the sin of egotism and goes ahead to commit it repeatedly. Proverbs 29:23 states that “arrogance will bring your downfall, but if you are humble, you will be respected.” When Slattery condemns Dante’s human state as being weak, doubtful, and limited, he is proving God’s hypocrisy because He is also human (Verdicchio, 2015). The actions of God in Hell as portrayed by Dante are inconsistent with the Biblical literature. Both Dante and God are prone to making mistakes, something common among human beings thus making God more human.

To wrap it up, Dante portrays God is more human since He commits the same sins that humans commit: egotism, hypocrisy, and injustice. Hell is justified as being a destination for victims of the mistakes committed by God. The Hell is presented as being a totally different place as compared to what is written about it in the Bible. As a result, reading through the text gives an image of God who is prone to the very mistakes common to humans thus ripping Him off His lofty status of divine and, instead, making Him a mere human. Whether or not Dante did it intentionally is subject to debate but one thing is clear in the poem: the misconstrued notion of God is revealed to future generations.

 

References

Babor, T. F., McGovern, T., & Robaina, K. (2017). Dante’s inferno: Seven deadly sins in scientific publishing and how to avoid them. Addiction Science: A Guide for the Perplexed, 267.

Cheney, L. D. G. (2016). Illustrations for Dante’s Inferno: A Comparative Study of Sandro Botticelli, Giovanni Stradano, and Federico Zuccaro. Cultural and Religious Studies4(8), 487.

Verdicchio, M. (2015). Irony and Desire in Dante’s” Inferno” 27. Italica, 285-297.