Hiring-Diagnostics

Robert W. Walker
November 6, 2017

The Problem

The HR Department needs a hiring diagnostic for choosing among applicants for employment. The goal is to maximize the productivity of chosen future employees by building and deploying a model for predicting and explaining worker productivity. We are to explain With as a function, potentially, of:

Dexterity: a diagnostic based on manual dexterity
General: a diagnostic based on general aptitude
Without: measured productivity over a four week period prior to introducing the device.
With: measured productivity over a four week period with the handheld device.

Summary Statistics

library(RcmdrMisc)
library(Rcmdr)
library(car)
numSummary(Hiring[,c("Dexterity", "General", "Subject", "With", "Without")], statistics=c("mean", "sd", "se(mean)", "IQR"))

              mean       sd se(mean)  IQR  n
Dexterity 176.0833 44.81860 7.469767 70.0 36
General   179.5556 54.06105 9.010175 90.0 36
Subject    18.5000 10.53565 1.755942 17.5 36
With      109.0000 12.24745 2.041241 20.0 36
Without   104.0000 12.98131 2.163551 20.0 36

Scatterplot Matrix

Our focus will be the third row.

plot of chunk unnamed-chunk-2

Regressions

library(stargazer)
Mod.DW <- lm(With~Dexterity+Without, data=Hiring)
Mod.GW <- lm(With~General+Without, data=Hiring)
Mod.DG <- lm(With~General+Dexterity, data=Hiring)
stargazer(Mod.DG,Mod.DW,Mod.GW, type="html")


	Dependent variable:

	With
	(1)	(2)	(3)

General	0.219^***		0.095^***
	(0.019)		(0.018)

Dexterity	-0.009	0.059^***
	(0.023)	(0.012)

Without		0.797^***	0.551^***
		(0.041)	(0.075)

Constant	71.286^***	15.670^***	34.560^***
	(2.935)	(3.664)	(5.148)


Observations	36	36	36
R²	0.888	0.955	0.957
Adjusted R²	0.881	0.952	0.955
Residual Std. Error (df = 33)	4.223	2.682	2.607
F Statistic (df = 2; 33)	130.667^***	348.301^***	369.641^***

Note:	^p<0.1; ^p<0.05; ^**p<0.01

Residuals

# Dexterity and General
shapiro.test(Mod.DG$residuals)


    Shapiro-Wilk normality test

data:  Mod.DG$residuals
W = 0.96384, p-value = 0.2816

# Dexterity and Without
shapiro.test(Mod.DW$residuals)


    Shapiro-Wilk normality test

data:  Mod.DW$residuals
W = 0.98128, p-value = 0.7876

# General and Without
shapiro.test(Mod.GW$residuals)


    Shapiro-Wilk normality test

data:  Mod.GW$residuals
W = 0.9639, p-value = 0.2828

The Plots [Seems Fine]

plot of chunk Plots

Which to Choose?

Without and General provide the best explanation. Without and Dexterity are a close second. General and Dexterity explain almost 90% but trail far behind.

From our chosen model, a few cool things….

A Plot

library(effects)
plot(allEffects(Mod.GW))

plot of chunk Plot1

A Prediction

Pred.Data <- data.frame(General=119, Without=86)
Pred.Data  # Newdata

  General Without
1     119      86

predict(Mod.GW, newdata=Pred.Data, interval="confidence", level=.95, 
  se.fit=FALSE)

      fit      lwr      upr
1 93.3029 91.76003 94.84578

predict(Mod.GW, newdata=Pred.Data, interval="prediction", level=.95, 
  se.fit=FALSE)

      fit      lwr      upr
1 93.3029 87.77848 98.82733

A Summary [in One Graphic]

A 3D Graphic