2. Bootstrap Simple Linear Regression Model
Ava DeStefano
Lecture Note: STA321 Topics of Advanced Statistics
1 Introduction
This data set was obtained from kaggle.com. The data set contains information on several thousand employees from an unnamed company. Since no details are given about the company, it cannot be said how exactly the data was collected. The response variable we are trying to predict is whether or no an employee stays at or leaves the company. The explanatory variables relate to each subjects work life. The response variable is whether or not an employee stays at or leaves the company. For my simple logistic regression analysis, the variable that I am going to use is “satisfaction_level”. This is the employees self reported satisfaction level.
1.1 Variable Description
- satisfaction_level (x1) - the employees self reported satisfaction level. (Numeric from 0-1)
- last_evaluation (x2) - the employees last performance review. (Numeric from 0-1)
- number_project (x3) - the number of projects an employee has done for the company. (Numeric)
- average_monthly_hours (x4) - the average number of hours an employee works per month. (Numeric)
- time_spend_company (x5) - how long the employee has worked at the company in years. (Numeric)
- Work_accident (x6) - number of work related accidents the employee has had. (Numeric)
- promotion_last_5years (x7) - Has the employee had a promotion in the last 5 years? (Binary 1=yes, 0=n0)
- Department (x8) - the department the employee is in. (categorical)
- Salary (x9) - salary level. (categorical)
- left (y) - whether the employee stays at or leaves the company (0=stay, 1=leave)
1.2 Practical Question
For this study, we want to identify which factors about an employee’s work life indicate they will leave the company.
1.3 Data Download
hr_data <- read.csv("https://raw.githubusercontent.com/AvaDeSt/STA-321/refs/heads/main/HR_comma_sep.csv", header = TRUE)
pred_vars <- select(hr_data, - "left")
data(hr_data) ## Warning in data(hr_data): data set 'hr_data' not foundhr.0 = hr_data
hr_d = na.omit(hr.0)
duplicates <- duplicated(hr_d)
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## [12217] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
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## [12337] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12349] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12361] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12373] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12385] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12397] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12409] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12421] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12433] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12445] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12457] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12469] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12481] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12493] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12505] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12517] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12529] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12541] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12553] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
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## [12649] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12661] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12673] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12685] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12697] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12709] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12721] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12733] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12745] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12757] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12769] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12781] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12793] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12805] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12817] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12829] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12841] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12853] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12865] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12877] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12889] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12901] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12913] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12925] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12937] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
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## [12961] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
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## [12985] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [12997] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13009] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13021] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13033] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13045] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13057] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13069] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13081] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13093] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13105] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13117] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13129] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13141] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13153] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13165] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13177] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13189] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13201] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13213] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13225] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13237] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13249] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13261] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13273] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13285] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13297] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13309] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13321] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13333] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13345] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13357] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13369] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13381] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13393] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13405] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13417] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13429] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13441] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13453] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13465] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13477] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13489] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13501] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13513] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13525] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13537] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13549] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13561] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13573] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13585] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13597] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13609] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13621] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13633] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13645] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13657] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13669] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13681] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13693] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13705] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13717] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13729] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13741] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13753] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13765] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13777] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13789] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13801] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13813] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13825] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13837] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13849] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13861] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13873] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13885] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13897] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13909] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13921] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13933] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13945] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13957] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13969] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13981] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [13993] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14005] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14017] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14029] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14041] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14053] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14065] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14077] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14089] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14101] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14113] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14125] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14137] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14149] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14161] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14173] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14185] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14197] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14209] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14221] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14233] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14245] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14257] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14269] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14281] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14293] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14305] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14317] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14329] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14341] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14353] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14365] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14377] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14389] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14401] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14413] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14425] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14437] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14449] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14461] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14473] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14485] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14497] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14509] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14521] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14533] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14545] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14557] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14569] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14581] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14593] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14605] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14617] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14629] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14641] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14653] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14665] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14677] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14689] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14701] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14713] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14725] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14737] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14749] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14761] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14773] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14785] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14797] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14809] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14821] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14833] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14845] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14857] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14869] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14881] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14893] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14905] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14917] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14929] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14941] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14953] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14965] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14977] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## [14989] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUEsum(duplicates)## [1] 3008hr <- unique(hr_d)The are no missing values in the data set. But there are 3008 duplicate values so I took those out of the data set.
2 Exploratory Analysis
data.num <- select(hr_data, "satisfaction_level", "last_evaluation", "number_project", "average_montly_hours", "time_spend_company") #data set of only the numeric variables
pairs.panels(data.num[,-9],
method = "pearson",
hist.col = "#00AFBB",
density = TRUE,
ellipses = TRUE
)
We can see from the graphs that the variable for the number of years
spent at the company is skewed. Here is a closer look:
par(mfrow=c(1,2))
hist(hr$time_spend_company, xlab="Years at the company", main = "")
To fix this, I am going to discretize “time_spend_company” based on the
histogram.
time = hr$time_spend_company
grp.time = time
grp.time[time %in% c(2:4)] = "2-4"
grp.time[time %in% c(5:7)] = "5-7"
grp.time[time %in% c(8:10)] = "8-10"
hr$grp.time = grp.timeThere is a moderate correlation between the number of projects and the average monthly hours an employee has worked. But since they are not too similar, they will both be kept for the time being. There is no need to transform any of the variables since we are only doing association analysis.
3 Model Building
full.model = glm(left ~ satisfaction_level + last_evaluation + number_project + average_montly_hours + Work_accident + promotion_last_5years + Department + salary + grp.time,
family = binomial(link = "logit"), # logit(p) = log(p/(1-p))!
data = hr)
kable(summary(full.model)$coef,
caption="Summary of inferential statistics of the full model")| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | -0.9867879 | 0.2450354 | -4.0271237 | 0.0000565 |
| satisfaction_level | -4.2525608 | 0.1242625 | -34.2224070 | 0.0000000 |
| last_evaluation | 0.5919079 | 0.1826236 | 3.2411352 | 0.0011905 |
| number_project | -0.3052465 | 0.0263733 | -11.5740741 | 0.0000000 |
| average_montly_hours | 0.0043584 | 0.0006329 | 6.8864733 | 0.0000000 |
| Work_accident | -1.4801817 | 0.1136691 | -13.0218516 | 0.0000000 |
| promotion_last_5years | -1.2925052 | 0.3859450 | -3.3489364 | 0.0008112 |
| Departmenthr | 0.0657740 | 0.1691216 | 0.3889154 | 0.6973387 |
| DepartmentIT | -0.0451906 | 0.1555504 | -0.2905204 | 0.7714181 |
| Departmentmanagement | -0.0866355 | 0.2069245 | -0.4186819 | 0.6754487 |
| Departmentmarketing | 0.0722944 | 0.1692217 | 0.4272169 | 0.6692214 |
| Departmentproduct_mng | -0.0514320 | 0.1672970 | -0.3074294 | 0.7585166 |
| DepartmentRandD | -0.4590236 | 0.1779200 | -2.5799431 | 0.0098817 |
| Departmentsales | 0.0447254 | 0.1318253 | 0.3392778 | 0.7344004 |
| Departmentsupport | 0.0902813 | 0.1396548 | 0.6464604 | 0.5179812 |
| Departmenttechnical | 0.0614581 | 0.1361925 | 0.4512593 | 0.6518027 |
| salarylow | 1.7717805 | 0.1653125 | 10.7177616 | 0.0000000 |
| salarymedium | 1.3334114 | 0.1665768 | 8.0047854 | 0.0000000 |
| grp.time5-7 | 1.3512536 | 0.0701784 | 19.2545459 | 0.0000000 |
| grp.time8-10 | -14.2440493 | 155.6796437 | -0.0914959 | 0.9270986 |
3.1 Reduced Model
reduced.model = glm(left ~ satisfaction_level + last_evaluation + number_project + promotion_last_5years + average_montly_hours + Work_accident,
family = binomial(link = "logit"), # logit(p) = log(p/(1-p))!
data = hr)
kable(summary(reduced.model)$coef,
caption="Summary of inferential statistics of the reduced model")| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | 0.3371415 | 0.1487394 | 2.266659 | 0.0234110 |
| satisfaction_level | -4.1861392 | 0.1201123 | -34.851889 | 0.0000000 |
| last_evaluation | 0.7862953 | 0.1752611 | 4.486422 | 0.0000072 |
| number_project | -0.2339762 | 0.0250456 | -9.342022 | 0.0000000 |
| promotion_last_5years | -1.4115858 | 0.3708276 | -3.806582 | 0.0001409 |
| average_montly_hours | 0.0042296 | 0.0006067 | 6.970990 | 0.0000000 |
| Work_accident | -1.3338246 | 0.1078854 | -12.363349 | 0.0000000 |
3.2 Final Model
final.model.forward = stepAIC(reduced.model,
scope = list(lower=formula(reduced.model),upper=formula(full.model)),
direction = "forward",
trace = 0
)
kable(summary(final.model.forward)$coef,
caption="Summary of inferential statistics of the final model")| Estimate | Std. Error | z value | Pr(>|z|) | |
|---|---|---|---|---|
| (Intercept) | -0.9779961 | 0.2147754 | -4.553576 | 0.0000053 |
| satisfaction_level | -4.2413818 | 0.1239701 | -34.212943 | 0.0000000 |
| last_evaluation | 0.5927693 | 0.1823071 | 3.251488 | 0.0011480 |
| number_project | -0.3046392 | 0.0263297 | -11.570158 | 0.0000000 |
| promotion_last_5years | -1.3257470 | 0.3845411 | -3.447608 | 0.0005656 |
| average_montly_hours | 0.0043328 | 0.0006318 | 6.857459 | 0.0000000 |
| Work_accident | -1.4841619 | 0.1136100 | -13.063650 | 0.0000000 |
| grp.time5-7 | 1.3416190 | 0.0700726 | 19.146130 | 0.0000000 |
| grp.time8-10 | -14.2350334 | 156.2040875 | -0.091131 | 0.9273885 |
| salarylow | 1.7761701 | 0.1647064 | 10.783859 | 0.0000000 |
| salarymedium | 1.3355641 | 0.1660276 | 8.044227 | 0.0000000 |
Even though we discovered that the number of projects an employee has and the average number of hours worked have a moderate correlation, the final model still includes both variables. We can see that the final mode only takes out the variable “Department”. The model stills keeps the variables for the number of years spent at the company “grp.time”, even though when time time spent at the company ranges from 8-10 years, the p-value is no longer significant.
global.measure=function(s.logit){
dev.resid = s.logit$deviance
dev.0.resid = s.logit$null.deviance
aic = s.logit$aic
goodness = cbind(Deviance.residual =dev.resid, Null.Deviance.Residual = dev.0.resid,
AIC = aic)
goodness
}
goodness=rbind(full.model = global.measure(full.model),
reduced.model=global.measure(reduced.model),
final.model=global.measure(final.model.forward))
row.names(goodness) = c("full.model", "reduced.model", "final.model")
kable(goodness, caption ="Comparison of global goodness-of-fit statistics")| Deviance.residual | Null.Deviance.Residual | AIC | |
|---|---|---|---|
| full.model | 8395.920 | 10781.18 | 8435.920 |
| reduced.model | 9005.841 | 10781.18 | 9019.841 |
| final.model | 8413.683 | 10781.18 | 8435.683 |
We can see that the final model has the lowest AIC, indicating it is the best one to use.
3.3 Odds Ratio
model.coef.stats = summary(final.model.forward)$coef
odds.ratio = exp(coef(final.model.forward))
out.stats = cbind(model.coef.stats, odds.ratio = odds.ratio)
kable(out.stats,caption = "Summary Stats with Odds Ratios")| Estimate | Std. Error | z value | Pr(>|z|) | odds.ratio | |
|---|---|---|---|---|---|
| (Intercept) | -0.9779961 | 0.2147754 | -4.553576 | 0.0000053 | 0.3760639 |
| satisfaction_level | -4.2413818 | 0.1239701 | -34.212943 | 0.0000000 | 0.0143877 |
| last_evaluation | 0.5927693 | 0.1823071 | 3.251488 | 0.0011480 | 1.8089912 |
| number_project | -0.3046392 | 0.0263297 | -11.570158 | 0.0000000 | 0.7373894 |
| promotion_last_5years | -1.3257470 | 0.3845411 | -3.447608 | 0.0005656 | 0.2656045 |
| average_montly_hours | 0.0043328 | 0.0006318 | 6.857459 | 0.0000000 | 1.0043422 |
| Work_accident | -1.4841619 | 0.1136100 | -13.063650 | 0.0000000 | 0.2266923 |
| grp.time5-7 | 1.3416190 | 0.0700726 | 19.146130 | 0.0000000 | 3.8252314 |
| grp.time8-10 | -14.2350334 | 156.2040875 | -0.091131 | 0.9273885 | 0.0000007 |
| salarylow | 1.7761701 | 0.1647064 | 10.783859 | 0.0000000 | 5.9071891 |
| salarymedium | 1.3355641 | 0.1660276 | 8.044227 | 0.0000000 | 3.8021401 |
The highest odds ratio belongs to the salarylow variable at 5.907. This means that when an employee has a low salary, their odds of leaving the company increase by about 5.907. (Although this does not instantly mean that having a low salary is the best indicator of if an employee leaves the company). The variable for time has three different categories with 2-4 as the base year. As the number of years spent at the company increases, the odds of leaving the company decreases.
4 Summary and Conclusion
To summarize, the data set we did an association analysis on looks at several factors affecting why an employee would leave a company. The data has nine explanatory variables. After discretising the variable “time_spend_company” into three dummy variables, there are eleven explanatory variables. We then built a full model, a reduced model, and a final model. Due to their high significance, all of the explanatory variables except for “Department” were kept in the final model. After calculating the odds ratios for each explanatory variable in the final model, we discovered that in regards to the time spent working at the company, as the number of years spent at the company increases, the odds of leaving the company decreases. To conclude, most of the variables in the data set could strongly indicate whether or not an employee would leave this certain company. This might suggest that other companies should look at things such as their employee satisfaction rate, and employee evaluation scores to predict if employees will stay with them or leave.
---
title: "2. Bootstrap Simple Linear Regression Model"
author: 'Ava DeStefano'
date: "Lecture Note: STA321 Topics of Advanced Statistics"
output:
  html_document: 
    toc: yes
    toc_depth: 4
    toc_float: yes
    fig_width: 4
    fig_caption: yes
    number_sections: yes
    toc_collapsed: yes
    code_folding: hide
    code_download: yes
    smooth_scroll: yes
    theme: lumen
  word_document: 
    toc: yes
    toc_depth: 4
    fig_caption: yes
    keep_md: yes
  pdf_document: 
    toc: yes
    toc_depth: 4
    fig_caption: yes
    number_sections: yes
    fig_width: 3
    fig_height: 3
editor_options: 
  chunk_output_type: inline
always_allow_html: true
---

```{=html}

<style type="text/css">

/* Cascading Style Sheets (CSS) is a stylesheet language used to describe the presentation of a document written in HTML or XML. it is a simple mechanism for adding style (e.g., fonts, colors, spacing) to Web documents. */

h1.title {  /* Title - font specifications of the report title */
  font-size: 24px;
  font-weight: bold;
  color: DarkRed;
  text-align: center;
  font-family: "Gill Sans", sans-serif;
}
h4.author { /* Header 4 - font specifications for authors  */
  font-size: 20px;
  font-weight: bold;
  font-family: system-ui;
  color: DarkRed;
  text-align: center;
}
h4.date { /* Header 4 - font specifications for the date  */
  font-size: 18px;
  font-weight: bold;
  font-family: system-ui;
  color: DarkBlue;
  text-align: center;
}
h1 { /* Header 1 - font specifications for level 1 section title  */
    font-size: 22px;
    font-weight: bold;
    font-family: system-ui;
    color: navy;
    text-align: left;
}
h2 { /* Header 2 - font specifications for level 2 section title */
    font-size: 20px;
    font-weight: bold;
    font-family: "Times New Roman", Times, serif;
    color: navy;
    text-align: left;
}

h3 { /* Header 3 - font specifications of level 3 section title  */
    font-size: 18px;
    font-weight: bold;
    font-family: "Times New Roman", Times, serif;
    color: navy;
    text-align: left;
}

h4 { /* Header 4 - font specifications of level 4 section title  */
    font-size: 18px;
    font-weight: bold;
    font-family: "Times New Roman", Times, serif;
    color: darkred;
    text-align: left;
}

body { background-color:white; }

.highlightme { background-color:yellow; }

p { background-color:white; }

</style>
```
```{r setup, include=FALSE}
# Detect, install and load packages if needed.
if (!require("knitr")) {
   install.packages("knitr")
   library(knitr)
}
if (!require("MASS")) {
   install.packages("MASS")
   library(MASS)
}
if (!require("nleqslv")) {
   install.packages("nleqslv")
   library(nleqslv)
}
#
if (!require("pander")) {
   install.packages("pander")
   library(pander)
}

if (!require("psych")) {   
  install.packages("psych")
   library(psych)
}
if (!require("MASS")) {   
  install.packages("MASS")
   library(MASS)
}
if (!require("tidyverse")) {   
  install.packages("tidyverse")
   library(MASS)
}

# specifications of outputs of code in code chunks
knitr::opts_chunk$set(echo = TRUE,      # include code chunk in the output file
                      warnings = FALSE,  # sometimes, you code may produce warning messages,
                                         # you can choose to include the warning messages in
                                         # the output file. 
                      messages = FALSE,  #
                      results = TRUE     # you can also decide whether to include the output
                                         # in the output file.
                      )   
```


# Introduction

This data set was obtained from kaggle.com. The data set contains information on several thousand employees from an unnamed company. Since no details are given about the company, it cannot be said how exactly the data was collected. The response variable we are trying to predict is whether or no an employee stays at or leaves the company. The explanatory variables relate to each subjects work life. The response variable is whether or not an employee stays at or leaves the company. For my simple logistic regression analysis, the variable that I am going to use is "satisfaction_level". This is the employees self reported satisfaction level.

## Variable Description 

* satisfaction_level (x1) - the employees self reported satisfaction level. (Numeric from 0-1)
* last_evaluation (x2) - the employees last performance review. (Numeric from 0-1)
* number_project (x3) - the number of projects an employee has done for the company. (Numeric)
* average_monthly_hours (x4) - the average number of hours an employee works per month. (Numeric)
* time_spend_company (x5) - how long the employee has worked at the company in years. (Numeric)
* Work_accident (x6) - number of work related accidents the employee has had. (Numeric)
* promotion_last_5years (x7) - Has the employee had a promotion in the last 5 years? (Binary 1=yes, 0=n0)
* Department (x8) - the department the employee is in. (categorical)
* Salary (x9) - salary level. (categorical)
* left (y) - whether the employee stays at or leaves the company (0=stay, 1=leave)

## Practical Question 

For this study, we want to identify which factors about an employee's work life indicate they will leave the company.


## Data Download 
```{r}
hr_data <- read.csv("https://raw.githubusercontent.com/AvaDeSt/STA-321/refs/heads/main/HR_comma_sep.csv", header = TRUE)


pred_vars <- select(hr_data, - "left")


data(hr_data)           
hr.0 = hr_data    
hr_d = na.omit(hr.0)

duplicates <- duplicated(hr_d)
print(duplicates)

sum(duplicates)

hr <- unique(hr_d)

```

The are no missing values in the data set. But there are 3008 duplicate values so I took those out of the data set. 

# Exploratory Analysis

```{r}
data.num <- select(hr_data, "satisfaction_level", "last_evaluation", "number_project", "average_montly_hours", "time_spend_company") #data set of only the numeric variables

pairs.panels(data.num[,-9], 
             method = "pearson", 
             hist.col = "#00AFBB",
             density = TRUE, 
             ellipses = TRUE 
             )
```
We can see from the graphs that the variable for the number of years spent at the company is skewed. Here is a closer look:

```{r}
par(mfrow=c(1,2))
hist(hr$time_spend_company, xlab="Years at the company", main = "")
```
To fix this, I am going to discretize "time_spend_company" based on the histogram.

```{r}
time = hr$time_spend_company
grp.time = time
grp.time[time %in% c(2:4)] = "2-4"
grp.time[time %in% c(5:7)] = "5-7"
grp.time[time %in% c(8:10)] = "8-10"

hr$grp.time = grp.time

```

There is a moderate correlation between the number of projects and the average monthly hours an employee has worked. But since they are not too similar, they will both be kept for the time being. There is no need to transform any of the variables since we are only doing association analysis. 

# Model Building 

```{r}
full.model = glm(left ~ satisfaction_level + last_evaluation + number_project + average_montly_hours + Work_accident + promotion_last_5years + Department + salary + grp.time, 
          family = binomial(link = "logit"),  #  logit(p) = log(p/(1-p))!
          data = hr)  
kable(summary(full.model)$coef, 
      caption="Summary of inferential statistics of the full model")
```

## Reduced Model 

```{r}
reduced.model = glm(left ~ satisfaction_level + last_evaluation + number_project + promotion_last_5years + average_montly_hours + Work_accident, 
          family = binomial(link = "logit"),  # logit(p) = log(p/(1-p))!
          data = hr) 
kable(summary(reduced.model)$coef, 
      caption="Summary of inferential statistics of the reduced model")
```

## Final Model

```{r}
final.model.forward = stepAIC(reduced.model, 
                      scope = list(lower=formula(reduced.model),upper=formula(full.model)),
                      direction = "forward",   
                      trace = 0   
                      )
kable(summary(final.model.forward)$coef, 
      caption="Summary of inferential statistics of the final model")
```


Even though we discovered that the number of projects an employee has and the average number of hours worked have a moderate correlation, the final model still includes both variables. We can see that the final mode only takes out the variable "Department". The model stills keeps the variables for the number of years spent at the company "grp.time", even though when time time spent at the company ranges from 8-10 years, the p-value is no longer significant.

```{r}
global.measure=function(s.logit){
dev.resid = s.logit$deviance
dev.0.resid = s.logit$null.deviance
aic = s.logit$aic
goodness = cbind(Deviance.residual =dev.resid, Null.Deviance.Residual = dev.0.resid,
      AIC = aic)
goodness
}
goodness=rbind(full.model = global.measure(full.model),
      reduced.model=global.measure(reduced.model),
      final.model=global.measure(final.model.forward))
row.names(goodness) = c("full.model", "reduced.model", "final.model")
kable(goodness, caption ="Comparison of global goodness-of-fit statistics")
```
We can see that the final model has the lowest AIC, indicating it is the best one to use. 

## Odds Ratio

```{r}
model.coef.stats = summary(final.model.forward)$coef
odds.ratio = exp(coef(final.model.forward))
out.stats = cbind(model.coef.stats, odds.ratio = odds.ratio)                 
kable(out.stats,caption = "Summary Stats with Odds Ratios")
```

The highest odds ratio belongs to the salarylow variable at 5.907. This means that when an employee has a low salary, their odds of leaving the company increase by about 5.907. (Although this does not instantly mean that having a low salary is the best indicator of if an employee leaves the company). The variable for time has three different categories with 2-4 as the base year. As the number of years spent at the company increases, the odds of leaving the company decreases. 

# Summary and Conclusion

To summarize, the data set we did an association analysis on looks at several factors affecting why an employee would leave a company. The data has nine explanatory variables. After discretising
the variable "time_spend_company" into three dummy variables, there are eleven explanatory variables. We then built a full model, a reduced model, and a final model. Due to their high significance, all of the explanatory variables except for "Department" were kept in the final model. After calculating the odds ratios for each explanatory variable in the final model, we discovered that in regards to the time spent working at the company, as the number of years spent at the company increases, the odds of leaving the company decreases. To conclude, most of the variables in the data set could strongly indicate whether or not an employee would leave this certain company. This might suggest that other companies should look at things such as their employee satisfaction rate, and employee evaluation scores to predict if employees will stay with them or leave. 